New Century Maths 10 Essentials - Chapter 09 - Probability

216

dropshadow

216

NUMBER

1In this chapter you will:

> text

dropshadow

216

NUMBER


> text

NUMBER


> text

dropshadow

216

NUMBER


> text

216

DATA


> ordercommonly-used‘chancewords’onanumberlinebetween0(impossible)and1(certain)

> listallpossibleoutcomesofasimpleeventandusetheterm‘samplespace’

> expresstheprobabilityofaneventAas

P(A)=numberofoutcomesmatchingtheeventtotalnumberofoutcomespossible

> expresstheprobabilityofaparticularoutcomeasafractionbetween0and1

> interpretanduseprobabilitiesexpressedaspercentagesordecimals

> recognisethatthesumoftheprobabilitiesofallpossibleoutcomesofasimpleeventis1

> identifythecomplementofaneventandfinditsprobability

> estimatetheprobabilityofaneventfromexperimentaldata,usingrelativefrequencies

> recognisethatprobabilityestimatesbecomemorestableasthenumberoftrialsincreases.

ProbabilityProbability

In this chapter you will:

> text


> text


> text

217

text

217

Wordbank

text

217

WordbankWordbank

What’s in Chapter 1?

Contents and syllabus referenCes examples

1-01 Mental addition NS3.2 (p.52)

23 + 918 + 14 + 32 + 6 + 9

1-02 Mental subtraction NS3.2 (p.52)

232 – 8220 – 135

ascending ordergoing up, from smallest to largest (1-2-3)decimal placesthe places after the decimal point in a decimaldescending ordergoing down, from largest to smallest (3-2-1)

differencethe answer to a subtractionestimateto make an educated guess of an answerevaluateto find the valuementalusing the mind




23 + 918 + 14 + 32 + 6 + 9


232 – 8220 – 135






23 + 918 + 14 + 32 + 6 + 9


232 – 8220 – 135




> text

text

217

Wordbank

217



9-01 The language of chanceNS3.5 (p. 73), NS4.4 (p. 74)

Use one of the following words to rate the probability of getting ‘tails’ when you toss a coin: impossible, unlikely, even chance, likely, certain.

9-02 Probability of a simple eventNS4.4 (p. 74)

Tom rolls a die. List the outcomes in the sample space. Find the probability of rolling a number greater than 4.

9-03 Complementary eventsNS4.4 (p. 74)

The probability of spinning yellow on a spinner is 15

.

What is the probability of spinning a colour that is not yellow?

9-04 Experimental probabilityNS5.1.3 (p. 75)

Emily surveyed families with 4 children and counted the number of girls in each family.

number of girls 0 1 2 3 4

frequency 5 17 42 20 16

If a 4-child family is selected at random, find: P(1 girl), P(more than 2 girls), P(1 boy)

9-05 Theoretical probabilityNS5.1.3 (p. 75)

Find the experimental and theoretical probabilities of drawing one card that is: diamonds, clubs, a black card. Why is there a difference between the experimental and theoretical probabilities? What should happen to the experimental probability if we drew one card 500 times?

complementary event all the outcomes that are not the event; the ‘opposite’ event. For example, the complementary event to ‘rolling 1 on a die’ is ‘rolling a number that is not 1’.diethe singular of dice (one die, 2 dice)even chanceequally likely to happen or not happen, ‘fifty-fifty’ chance,

probability of 12

eventa result involving one or more outcomes. For example, the event of rolling an even number on a die contains the three outcomes {2, 4, 6}.experimental probabilityprobability based on an experiment over repeated trials, based on relative frequency; an estimate of theoretical probability

probabilitythe chance of an event occurring, measured as a fraction, decimal or percentage between 0 and 1randomdescribing a situation where each possible outcome has equal chancesample spacethe set of all possible outcomes of a situation or experiment

Wordbank

218 maths essentials 10218218

EXAMPLE 1Use one of the words in the above table to rate the chance of each of the following events.a A new-born baby being a boy.b Living on the moon next week.c A chicken came from an egg.d A person who bets on a horse in a race wins.e An adult person knows how to drive a car.

SOLUTIONa Even chance b Impossible c Certaind Unlikely e Likely

EXAMPLE 2Place the following terms in an appropriate position on the probability scale below. a Probably b Rarely c Sure bet d Fifty-fifty

12

0 1

impossible certain

SOLUTION

12

0 1

impossible

rarely fifty-fifty probably sure bet

certain

The language of chanceThe language of chance9 - NS3.5, 4.4

Probability means ‘chance’. The chance of an event happening can be written as a fraction.

For example, the probability of flipping a coin and having it land ‘heads’ is 12

. This table shows

some common terms for describing the chances of something occurring.

term meaning example

impossible Will not happen, probability of 0 It will snow on Bondi Beach.

unlikely Probably won’t happen; a low chance of happening

Winning a prize in a competition.

even chance Equally likely to happen or not happen; ‘fifty-fifty’ chance;

probability of 12

Flipping ‘heads’ on a coin.

likely Probably will happen; a good chance of happening

A family chosen at random has one or two children.

certain Will happen; will definitely occur; probability of 1

It will get dark tonight.

9 Probability 219

1 Rate each of these events as impossible, certain, unlikely, likely, or even chance.a You will see a live dinosaur.b A die is rolled and an odd number comes up.c You pick a red lolly from a bag of red lollies.d The next baby born is a girl.e The next car to go past the school is green.f You will finish Year 10.

2 Draw a probability scale like the one below. Make it 15 cm long and mark the position of each of the following terms in an appropriate position.

not likely fair chance no way definitely probably unusual always quite often even chance likely never hardly

12

0 1

impossible certain

3 Draw another probability scale and place the following letters (A, B, etc.) to show the likelihood of each event.A An Ace is chosen from a pack of playing cards.B From a box of dark chocolates, you choose a white chocolate.C There will be a hail storm tomorrow.D A person selected at random has a birthday on a weekday, not on the weekend.E A double six is rolled on a pair of dice.F There will be no car accidents in Sydney tomorrow.G You play Lotto and win first prize.H You will eat pizza next month.I Somebody’s house has a computer.

4 ‘Buckley’s chance’ is an Australian expression meaning little or no chance.a Write a probability value for Buckley’s chance.b Give an example of an event that could have Buckley’s chance.

Exercise 9-01worksheet

9- 01Chance cards

die is the singular of dice. Two dice, one die.


NS4.4

9 - Probability of a simple eventProbability of a simple event

EXAMPLE 3Tom rolls a die and notes the number that comes up. a List the outcomes in the sample space.b Find the probability of rolling a number greater than 4.

SOLUTIONa The sample space is: {1, 2, 3, 4, 5, 6} 6 possible outcomesb The numbers greater than 4 are: {5, 6} 2 outcomes

P(number 4) = 26

= 13

EXAMPLE 4A card is chosen at random from a set of cards numbered 0 to 9.a List the outcomes in the sample space.b Write as a decimal the probability of choosing an odd number.c Write as a percentage the probability of choosing a number less than 3.

SOLUTIONa The sample space is: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} 10 possible outcomesb The odd numbers are: {1, 3, 5, 7, 9} 5 outcomes

P(odd number) = 510

= 0.5

c The numbers less than 3 are {0, 1, 2}. 3 outcomes

P(number 3) = 310

= 310

× 100% = 30%

At random means that each card has an equal chance of being chosen.

In probability situations, the set of all possible outcomes is called the sample space. For

example, when a coin is flipped, the sample space is {heads, tails}. If each outcome has

equal chance, then numerical values can be assigned to probabilities.

ProbabilityThe probability of an event E is:

P(E) = number of outcomes matching the event

total number of outcomes possible

An event can consist of one or more outcomes. The probability of an event can be written as

a fraction, decimal or percentage. For example, the probability of flipping heads on a coin can

be written as 12

, 0.5 or 50%.

9 Probability 221

1 For each spinner: i write the sample space of possible outcomes ii find the probability that the arrow will land on blue.

a b c

2 A packet of jelly beans contains 5 yellow, 4 red, 8 green and 3 black jellybeans. Anna picks one jelly bean at random.a List the sample space.b Which colour is Anna most likely to pick?c What is P(yellow) as a decimal?d What is P(red or green) as a percentage?e What is P(not green) as a simple fraction?

3 A die is rolled. Find (as a fraction) the probability of: a rolling a 5 b rolling a 3 or 4 c not rolling a 3 or 4.

4 A piggy bank contains four 10-cent coins, five 20-cent coins, one 50-cent coin, three $1 coins and three $2 coins. A coin is chosen at random. Find as a percentage the probability that the coin is:a 10 cents b 50 cents c a gold coin d not 20 cents.

5 Match each probability value (a to d) with the best description (A to D).a 0.01 b 70% c 100% d 0.3A probable B sure C not likely D rare chance

6 All of the letters of the alphabet are placed in a box. Tyrone picks out one letter. Find:a P(K) b P(Y or Z) c P(a vowel) d P(letter before E)

7 Paul says that because there are 12 teams in the rugby competition, the probability that the

Waratahs will win is 112

. Why is Paul incorrect in saying this?

8 A normal deck of cards has 52 cards divided into 4 suits (hearts, diamonds, clubs, spades) of 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). If one card is chosen from a deck, find the probability that it is:a a King b a heart c red d a black 10e a picture card (Jack, Queen, King) f a black card or a 2 g not a 7.


9- 02Probability problems

worksheet9- 03

Games of chance


9 -

EXAMPLE 5This spinner is spun.a Find P(yellow).b What is the complementary event to spinning yellow?c What is the probability of not spinning yellow?

SOLUTION

a P(yellow) = 15

b The complementary event to spinning yellow is not spinning yellow, that is, spinning red, blue, green or orange.

c P(not yellow) = 1 – P(yellow)

= 1 – 15

= 45

EXAMPLE 6A bag contains 3 blue, 2 white and 4 red marbles. One marble is drawn at random. Find:a P(red) b P(not red) c P(green) d P(not blue).

SOLUTION

a P(red) = 49

The total number of marbles is 3 + 2 + 4 = 9.

b P(not red) = 1 – P(red) = 1 – 49

= 59

c P(green) = 09

= 0

d P(not blue) = 1 – P(blue) = 1 – 39

= 23

Complementary eventsComplementary eventsNS4.4

Probability is measured on a scale from 0 (impossible) to 1 (certain). In any situation, the

probabilities of all possible outcomes must add up to 1. For example, if the probability of

rolling 4 on a die is 16

, then the probability of not rolling 4 is 56

, because 16

+ 56

= 1.

The word complement means something that completes or goes with something. In relation

to probability, the complement of an event E means all those outcomes that are not E, or the

opposite of E. For example, the complement of ‘rolling 4’ is ‘not rolling 4’ (that is, rolling 1, 2,

3, 5 or 6).

Complementary eventsP(E) + P(not E) = 1

P(complementary event) = 1 – P(event)

P(event not occurring) = 1 – P(event occurring)

VIDEO 17

9 Probability 223

1 What is the complementary event for each of these events? Write the answer in words.a Tossing a coin and getting tailsb Picking a clubs card at random from a deck

of cardsc Rolling a number greater than 2 on a died Picking a red ball at random from a bag of

white, red and blue ballse Coming first in a racef Winning a soccer match

2 Copy and complete the following complementary probabilities.a When rolling a die: b When choosing from a deck of cards: P(greater than 2) = 1 – P(__________) P(not a Jack) = 1 – P(__________)

= 1 – 26

= 1 – ___

= ___ = ___

3 The probability that a netball team will win a game is 23

. Find the probability that the team will not win.

4 An archer has a 60% chance of hitting the bullseye. What is the probability that he misses the bullseye?

5 The probability of dying in a plane crash is 0.000 05. What is the probability of not dying in a plane crash?

6 A jar contains 7 yellow, 2 green and 3 purple lollies. If a lolly is selected at random, find:a P(yellow) b P(not yellow) c P(green) d P(not green)e P(red) f P(not red) g P(not purple) h P(not white).

7 The probability that it will not rain this weekend is 78%. Find the probability that it will rain this weekend.

8 What is the probability that a student selected at random from your school was born in a month not beginning with J?

9 Janelle bought 4 tickets in a raffle where 500 tickets were sold. What is the probability that Janelle:a wins first prize? b does not win first prize?

10 A packet contains seeds for yellow, white and mauve flowers. P(yellow flower) = 0.3 and P(mauve flower) = 0.1. If a seed is planted find:a P(yellow or mauve flower) b P(white flower)c P(not a yellow flower) d P(not a pink flower).

Exercise 9-03


9 - Experimental probabilityExperimental probabilityNS5.1.3

EXAMPLE 7Emily surveyed families with 4 children and counted the number of girls in each family. The results are shown in this table.

number of girls 0 1 2 3 4

frequency 5 17 42 20 16

Based on these results, if a 4-child family is selected at random, find:a P(1 girl) b P(more than 2 girls) c P(1 boy) d P(at least 1 girl).

SOLUTIONTotal number of families surveyed = 5 + 17 + 42 + 20 + 16 = 100

a P(1 girl) = 17100

b P(more than 2 girls) = P(3 or 4 girls)

= 20 + 16100

= 36100

= 925

c P(1 boy) = P(3 girls) In a 4-child family, if there is 1 boy, there must be 3 girls.

= 20100

= 15

d P(at least 1 girl) = P(1, 2, 3 or 4 girls) = P(not 0 girls) ‘At least one’ means ‘not none’. = 1 – P(0 girls)

= 1 – 5100

= 1920

Experimental probability is based on the results of an ‘experiment’ or trial that has been

repeated many times. For example, a trial could involve testing a light globe to see whether it

works, or measuring a person’s heartbeat rate. The trial is repeated for many light globes or

many people.

The experimental probability of an event is the relative frequency of the event during the

total number of trials.

Experimental probability P(E) =

number of times the event happenedtotal number of trials

= frequency of the event

total frequency

VIDEO 18

The relative frequency is how many times an event occurred, written as a fraction of the total number of trials.

9 Probability 225

1 Evie tossed a coin many times and got 140 heads and 110 tails. Based on these results, what is the experimental probability of tossing tails with this coin?

2 Khalil surveyed students in all Year 10 classes to find out their favourite type of music for the school dance. The results were rock 24, rap 21, R&B 25 and pop 50. Find the probability that a Year 10 student selected at random:a likes pop best b likes rock or rap best c does not like pop best.

3 The table below shows the number of babies born per day at a maternity hospital during the month of January.

number of babies 0 1 2 3 4 5

frequency 1 4 7 10 5 4

Find the probability that on a day in January selected at random:a 2 babies were delivered b 4 or 5 babies were deliveredc fewer than 3 babies were delivered d at least one baby was delivered.

4 A coloured spinner was spun 600 times. The results are shown in the table.

Colour frequency

Green 99

White 201

Black 198

Orange 102

a Find the experimental probability of spinning: i green ii black or orange iii not white.

b Copy the spinner and colour the sectors to match the experimental probabilities shown in the table.

5 Toss two coins together 120 times. Copy the table below and record your results:

event frequency

2 heads

A head and a tail

2 tails

Total 120

a Use your results to find each of these experimental probabilities. i P(2 heads) ii P(2 tails) iii P(a head and a tail) iv P(at least one head)

b Why does tossing a head and a tail have about double the chance of tossing 2 heads?


9- 04A page of spinners

worksheet9- 05

Spinner game

worksheet9- 06

Dice probability

worksheet9- 07Greedy pig game


9 - Theoretical probabilityTheoretical probabilityNS5.1.3

Experimental probability is only an estimate of the actual or theoretical probability of an

event. The formula for theoretical probability is:


total number of outcomes possibleThis formula works only if all possible outcomes in the sample space have an equal chance of

happening.

If the trials of an experiment are repeated often, the value of the experimental probability will

get closer to the theoretical probability. In the long run, the more trials there are, the more

accurate the experimental probability. This is sometimes called ‘the law of averages’.

EXAMPLE 8Alice picked one card at random from a normal deck. She recorded the suit of the card, and then returned it to the deck. Alice did this 160 times. Her results were: hearts 35 times, diamonds 32 times, clubs 44 times, spades 49 times.a Find (as a decimal) the experimental and theoretical probabilities of drawing: i diamonds ii clubs iii a black card.b Why is there a difference between the experimental and theoretical probabilities?c What should happen to the experimental probabilities if Alice drew a card from

the deck 500 times?

SOLUTION

a

experimental probability theoretical probability

i P(diamonds) 32160

= 0.21352

= 14

= 0.25

ii P(clubs) 44160

= 0.2751352

= 14

= 0.25

iii P(black card) 44 + 49160

= 0.581252652

= 12

= 0.5

b Experimental probability is only an estimate or approximation of theoretical probability.

c With a greater number of trials, the experimental probabilities will get closer to the theoretical probabilities. For example, the chance of drawing a diamonds card will get closer to 0.25.

EXAMPLE 9a Why is the following statement incorrect? ‘This spinner has 5 possible outcomes so the probability

of spinning an 8 is 15

.’

b What is the probability of spinning 8 on this spinner?

9 5

84

2

SOLUTIONa Not all outcomes have equal chance. Spinning 9 is twice

as likely as spinning any other number.b There are 6 equal regions on the spinner.

P(spinning 8) = 16

5

84

2

9

9 Probability 227

1 The numbers from 1 to 10 are each written on a card and put into a barrel. Luis selects one card at random. Find the probability that he selects: a 9 b an even number c a multiple of 3d 5 or below e a number less than 5 f neither 1 nor 10.

2 What is wrong with the following statement? ‘The probability of a traffic light being amber (orange) is 1

3 because there are 3 outcomes in the

sample space for a traffic light: red, amber and green’.

3 Samir tossed a coin 120 times and it came up heads 54 times.a What is Samir’s experimental probability of tossing heads, as a percentage?b What is the theoretical probability of tossing heads?c How can Samir improve his experimental probability to be closer to 50%?

4 If a die is rolled 300 times, how many times would you expect a 2 to come up?

5 Becky and Sarah play a game where a card is picked at random from a standard deck. If the card is an Ace, Becky wins. If it is a heart, Sarah wins.a Find the probability that:

i Becky wins ii Sarah wins iii neither girl wins.b Is a draw possible; that is, could both girls win? Give a reason for your answer.c Is this game fair? Give reasons.

6 Copy this spinner. Write a different number in each of its five sections so that the probability of spinning a number greater than 10 is 0.8.

7 Simone thought that, because there were 6 candidates for school captain, each candidate had a 16

chance of being elected captain. Why is this incorrect?

8 Using H for heads and T for tails, the sample space when 3 coins are tossed together is{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Find the probability of tossing:a all heads b 2 tails c 2 heads d all tails e at least one head.

9 The letters of the words NEW CENTURY are written on separate cards and placed in a bag. Kai draws one out at random and wins $10 if it shows a vowel (A, E, I, O or U).

a Kai says that the probability of winning must be 14

because there are 2 vowels and 6 consonants

in NEW CENTURY. Comment on this statement.b What is the theoretical probability that Kai wins?

10 A die is ‘loaded’ so that the chance of rolling a 6 is double the chance of rolling each of the other numbers. What is the probability of rolling:a a 6? b a 5? c an even number? d an odd number?


9- 08Matching probabilities

worksheet9- 09

Probability review

228 maths essentials 10228 maths essentials 10228 maths essentials 10228 maths essentials 10228 maths essentials 10

Using technologyUsing technology

spreadsheet1

ordering decimals


spreadsheet1

ordering decimals


spreadsheet1

ordering decimals

spreadsheet1

ordering decimals

Using technologyUsing technologyUsing technologyUsing technologyCoin-tossing simulation

A simulation is an experiment that models a real thing. You can generate random numbers on a spreadsheet to model tossing a coin.

A

1 Tossing a coin2 =INT(RAND( )*2+1)

Step 1: Click on the icon. Type the formula in cell A2 and the spreadsheet will randomly show either the number 1 (heads) or the number 2 (tails). A

1 Tossing a coin2 13 24 2

…

Step 2: ‘Fill down’ the formula from A2 to A11. This will simulate tossing a coin 10 times. Copy the table below, count the number of heads (1) and tails (2) on your spreadsheet, and write the totals in the ‘Trial 1’ column.

trial 1 2 3 4 5 6 7 8 9 10 Total

Heads

tails

Step 3: Press the F9 key or select the ‘Recalculate’ function to generate another set of 10 random numbers. Repeat until you have generated 100 random numbers, writing the totals for each trial in the table.

Step 4: How many heads and tails did you expect from 100 tosses?

Step 5: Are your results what you expected? Explain the differences.

spreadsheet9

Coin-tossing simulation

Skillbank 1Skillbank 1

skilltest1

decimals


skilltest1

decimals


skilltest1

decimals

Skillbank 1Skillbank 1Skillbank 9Skillbank 9Dividing a quantity in a given ratio 1 Examine this example: Divide $450 between Jennie and Tim in the ratio 4 : 5. Total number of parts = 4 + 5 = 9 1 part = $450 ÷ 9 = $50 Jennie’s share = 4 × $50 = $200 Tim’s share = 5 × $50 = $250 Check: $200 + $250 = $450 (original amount)

2 Now divide each of these quantities in the given ratio:a Divide $7000 between Callum and Sophia in the ratio 4 : 3b Divide $660 between Jai and Loretta in the ratio 1 : 5c Divide $1800 between Daniel and Sabina in the ratio 2 : 1d Divide $3200 between Sara and Dave in the ratio 3 : 5e Divide $400 between Tan and Jess in the ratio 4 : 1f Divide $2700 between Aaron and Jude in the ratio 7 : 2

To practise dividing a quantity in a given ratio, click on the ‘Skilltest 9’ icon.

skilltest9

Dividing a quantity in a given ratio

229

Chapter summary: Chapter summary

1 Non-calculator maths 229








9 Probability

Probability

See also Wordbank at the

front of this chapter.

9-01 The language of chanceProbability can be measured on a scale between 0 (impossible) and 1 (certain).Unlikely: low chance, probably won’t happenEven chance: equally likely to happen or not happen,

‘fifty-fifty’ chance, probability of 12

Likely: good chance, probably will happen

9-02 Probability of a simple eventSample space: the set of all possible outcomesEvent: a result involving one or more outcomesThe probability of an event E is:


total number of outcomes possibleThe sample space for rolling a die is {1, 2, 3, 4, 5, 6} and the odd outcomes are {1, 3, 5}.

\ P(odd number) = 36

= 12

Probabilities can be expressed as fractions, decimals or percentages.

9-03 Complementary eventsThe probabilities of all possible outcomes (in the sample space) must add up to 1.The complement of an event is all those outcomes not in the event or the opposite of the event.The complementary event to ‘rolling an even number’ on a die is ‘rolling an odd number’.P(E) + P(not E) = 1P(complementary event) = 1 – P(event)P(event not occurring) = 1 – P(event occurring)

If P(rain today) = 0.64, P(no rain today) = 1 – 0.64 = 0.36

9-04 Experimental probabilityThe experimental probability of an event is based on the number of times an event occurred during a number of trials.

P(E) = number of times the event happened

total number of trials

= frequency of the event

total frequencyA coin was tossed 120 times and heads came up 57 times. The experimental probability of tossing

heads is: 57

120 =

1940

9-05 Theoretical probability


total number of outcomes possibleThis formula works only if all possible outcomes in the sample space have an equal chance of happening.Experimental probability is an estimate of the theoretical probability. The greater the number of trials, the closer the experimental probability is to the theoretical probability.

worksheet9- 10

Probability crossword


Practice test 9SECTION 1

Calculators are not allowed.

1 Evaluate: 0.2 × 0.4 2 Find the median of: 3, 4, 6, 9, 10, 10

3 Evaluate: 32 + 42 4 Simplify: m2 + m2

5 Find: 1% of $340 6 Simplify 3 cm : 6 m

7 What part of a circle 8 Write the value of tan q in this triangle. is indicated by the arrow? 13

5

12

9 Solve: 4 – 2m = –12

10 How long does it take a truck to travel 240 km at a speed of 80 km/h?

SECTION 2 – Part A

Calculators are allowed. Select the correct answer A, B, C or D.

11 A term that describes an event with a ‘fifty-fifty’ chance is:A impossible B probable C likely D even chance.

12 What is the complementary event of choosing a diamond from a deck of playing cards?A Choosing a black card B Choosing a heart C Choosing a picture card D Choosing a card that is not a diamond

13 The probability that it will rain tomorrow is 44%. What is the probability that it won’t rain?A 56% B 88% C 45% D 6%

14 The probability of rolling a number greater than 3 on a die is:

A 12

B 13

C 23

D 34

15 Which one of these probabilities describes an event that is unlikely to happen?A 0.2 B 0.5 C 0 D 0.55

16 A coin is tossed 60 times and heads comes up 36 times. The experimental probability of tails coming up is:

A 60% B 0.4 C 35

D 3460

2319 Probability

17 On which spinner are P(red) and P(blue) not equally likely?

A B C D

18 Jasmine tosses a coin and a die together. The sample space (using H for heads and T for tails) is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.What is the probability that Jasmine tosses a tail and an odd number?

A 16

B 14

C 13

D 12

19 The probability of an event that is certain to happen is:A 100 B 1 C 0 D 0.5

20 This spinner has a missing number. Which of the following could be the missing number if P(a number greater than 8) = 40%?A 6 B 9 C 11 D 12

7 9

?

10

5

Questions 21–22 may have more than one answer. Select all correct answers.

21 Which of the following terms could describe a probability greater than 0.5?A A slim chance B A ‘fifty-fifty’ chanceC Certain D Highly likely

22 A ball is drawn out of a bag containing 5 red, 1 white and 4 green balls. Which of the following statements are true?A P(red) = 50% B P(not white) = 10%C P(red or white) = 60% D P(blue) = 0%

SECTION 2 – Part B

Calculators are allowed.

23 Sixty families with 2 children were surveyed on the number of boys in the family. The results are shown in the table.

number of boys 0 1 2

frequency 12 30 18

Based on these results, find the probability that a family of 2 children will have:a 2 boys b 1 boy c 2 girls d at least 1 boy.

24 The letters of the word ESSENTIALS are written on cards and placed in a hat. One card is chosen at random.a How many possible outcomes are there in the sample space?b Find the probability of choosing the letter E.c Find the probability of choosing a letter that is not a vowel.d Jack says that the probability of choosing a vowel or a repeated letter is 7

10.

Is he correct? Give a reason for your answer.

test 9

Documents

New Century Maths 10 Essentials - Chapter 09 - Probability