WorkSHEET 13.1 Probability Name: · WorkSHEET 13.1 Probability Name: _____ 1 Are the following statements true or false? (a) The events of choosing a red card, or a black card, from

© John Wiley & Sons Australia, Ltd 2012 Page 1

WorkSHEET 13.1 Probability I Name: ___________________________ 1 List the sample space of:

(a) a 6-sided die (b) a coin.

Answers: (a) S={1, 2, 3, 4, 5, 6} (b) S={H,T}

2 You are tossing a coin. What is the probability of you tossing a head?

Start with listing the Sample Space:

𝑆 = {𝐻, 𝑇} → 𝑃𝑂 = 2 The sample space gives you how many possible

outcomes (PO) you have … here it is 2 … so you know PO is 2

From the Sample Space, look to find how many

Wanted Outcomes (WO) there are … here there is only one Head, hence WO is 1

Then state the rule;

𝑃 =𝑊𝑂𝑃𝑂

=12

It’s not much to ask, so please state the rule

each time you use it J


3 You are rolling a standard die. What is the probability you roll a 6?

Start with listing the Sample Space:

𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6 The sample space gives you how many possible

outcomes (PO) you have … here it is 6 … so you know PO is 6

From the Sample Space, look to find how many

Wanted Outcomes (WO) there are … here there is only one number 6, hence WO is 1

Then state the rule;


=16

It’s not much to ask, so please state the rule

each time you use it J


4 When you roll a die, what is the probability of rolling a:

a) Rolling a 5 b) Rolling a 2 c) Rolling a 2 or a 5 d) Rolling a number bigger than 4

First, list the Sample Space

𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6 a)


=16

b)


=16

c)


=26

=13

d)


=26

=13

** Yes, always state the rule before you use it! ** Yes, you always need to simplify your

answer!



a) Rolling an even number

b) Rolling a number smaller than 3

c) Rolling a number at least 3

d) Rolling a number at most 3


𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6 a)


=36

=12

b)


=26

=13

c)


=46

=23

d)


=36

=12


6 There are 3 green, 2 red and 5 yellow balls in a bag. What is the chance you pull out a:

a) Pulling out a green ball

b) Pulling out a yellow ball

c) Pulling out a yellow or a green ball

d) Pulling out a ball that is NOT green


𝑆 = {3𝐺, 2𝑅, 5𝑌} → 𝑃𝑂 = 10 a)


=310

b)


=510

=12

c)


=810

=45

d)


=710


7 You draw a card, from a standard deck of cards. What is the chance you draw a:

a) Draw a red card

b) Draw a Club

c) Draw a 10

d) Draw a red 5

First, list the Sample Space 𝑆 = {𝑑𝑜𝑛!𝑡𝑛𝑒𝑒𝑑𝑡𝑜𝑙𝑖𝑠𝑡𝑡ℎ𝑒𝑠𝑒} → 𝑃𝑂 = 52 a)


=2652

=12

b)


=1352

=14

c)


=452

=113

d)


=252

=126


8 What is the chance a person’s birthday falls on a Sunday this year?


𝑆 = {𝑀, 𝑇,𝑊, 𝑇, 𝐹, 𝑆, 𝑆} → 𝑃𝑂 = 7


=17

9 What is the chance a person’s birthday falls on a day starting with the letter T?


𝑆 = {𝑀, 𝑇,𝑊, 𝑇, 𝐹, 𝑆, 𝑆} → 𝑃𝑂 = 7


=27

10 Terry rolls a die. What is the chance he rolls a 3? 𝑃 =

𝑊𝑂𝑃𝑂

=16

11 Terry rolls a die. What is the chance he rolls a an even number?

𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6

𝑐𝑜𝑢𝑛𝑡ℎ𝑜𝑤𝑚𝑎𝑛𝑦𝑒𝑣𝑒𝑛𝑠 → 𝑊𝑂 = 3


=36

=12


12 Terry rolls a die. What is the chance he rolls a number larger than 4?

𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6

𝑐𝑜𝑢𝑛𝑡ℎ𝑜𝑤𝑚𝑎𝑛𝑦𝑏𝑖𝑔𝑔𝑒𝑟𝑡ℎ𝑎𝑛4 (5𝑎𝑛𝑑6) → 𝑊𝑂 = 2


=26

=13

13 Kelsey draws from a standard deck of cards. What is the chance she draws a red card?

𝑆 = {52𝑐𝑎𝑟𝑑𝑠𝑖𝑛𝑎𝑑𝑒𝑐𝑘} → 𝑃𝑂 = 52

𝑐𝑜𝑢𝑛𝑡ℎ𝑜𝑤𝑚𝑎𝑛𝑦𝑟𝑒𝑑 → 𝑊𝑂 = 26


=2652

=12

14 Kelsey draws from a standard deck of cards. What is the chance she draws a red Ace?

𝑆 = {52𝑐𝑎𝑟𝑑𝑠𝑖𝑛𝑎𝑑𝑒𝑐𝑘} → 𝑃𝑂 = 52 𝑐𝑜𝑢𝑛𝑡ℎ𝑜𝑤𝑚𝑎𝑛𝑦𝑟𝑒𝑑𝐴𝑐𝑒𝑠 → 𝑊𝑂 = 2


=252

=126


15 Kelsey draws from a standard deck of cards. What is the chance she draws a 10?

𝑆 = {52𝑐𝑎𝑟𝑑𝑠𝑖𝑛𝑎𝑑𝑒𝑐𝑘} → 𝑃𝑂 = 52

𝑐𝑜𝑢𝑛𝑡ℎ𝑜𝑤𝑚𝑎𝑛𝑦10′𝑠 → 𝑊𝑂 = 4


=452

=113

16 Experimental Probability - Relative Frequency

17 An Archer has 17 shots at the target and hits the bullseye 3 times. What is the relative frequency of him hitting the bullseye?

𝑅𝐹 =#𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠#𝑇𝑟𝑖𝑎𝑙𝑠

=317

18 A cricketer has 11 shots at the stumps and hits them 8 times. What is the likelihood the cricketer will hit the stumps on their next shot?


=811

19 A footballer has 27 shots at goal and scores 25 times. What is the probability the footballer will score a goal on their next shot?


=2527

20 Belinda is practicing her hockey shots at goal. If she shoots 9 goals out of 10 attempts, what is the relative frequency of her making a goal?


=910

21 Bazza is throwing tennis balls at his brother. If he hits his brother 7 times out of 9 shots, what is the relative frequency of her making a goal?


=79


22 The Additive Rule of Probability

“OR” is “PLUS”

23 When you roll a die, what is the probability of rolling a 2 or a 3?


𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6


=26

=13

24 Same as the previous question, you are rolling a standard die. What is the probability you roll a 2 or a 3?

Lets do this differently, by using the additive rule of probability;

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

𝑃(2 ∪ 3) = 𝑃(2) + 𝑃(3)

=16 +

16

=26

=13

That’s the additive rule of probability!


25 When you draw a card, what is the probability it is either a 10 or a 3 of diamonds?

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

𝑃(10 ∪ 3𝐷) = 𝑃(10) + 𝑃(3𝐷)

=452 +

152

=552

26 In a year 8 cross country race, the probability of Bill winning the race is "

# and the

probability of Susan winning the race is "$ .

Calculate the probability that either Bill or Susan win the race.

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

=18 +

12

=58

27 The probability it will be sunny today is 0.64 and the chance of clouds is 0.23. What is the chance it is sunny or cloudy today?

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

= 0.64 + 0.23 = 0.87

28 The probability Derwood will do his Maths homework is 0.09 and the chance Derwoord will do his English homework is 0.7. What is the probability that Derwood will do either his English or Maths homework?

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

= 0.7 + 0.09 = 0.79

29 There are 3 green, 2 red and 5 yellow balls in a bag. What is the chance you pull out a:

a) Pulling out a yellow or a green ball


𝑆 = {3𝐺, 2𝑅, 5𝑌} → 𝑃𝑂 = 10 z)


=810

=45


30 Validate your last answer by is a Probability Rule.

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

=510 +

310

=810

=45


a) Rolling a 5 or a 6


=26

=13

32 Validate your last answer by is a Probability Rule.

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

𝑃(5𝑜𝑟6) = 𝑃(5) + 𝑃(6)

=16 +

16

=13

33 Terry rolls a die. What is the chance he rolls a 2 or a 3?

𝑆 = {1, 2, 3, 4, 5, 6} → 𝑃𝑂 = 6 𝑐𝑜𝑢𝑛𝑡ℎ𝑜𝑤𝑚𝑎𝑛𝑦2!𝑠𝑎𝑛𝑑3′𝑠 → 𝑊𝑂 = 2


=26

=13


34 Justify your previous solution using a probability rule.

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

𝑃(2𝑜𝑟3) = 𝑃(2) + 𝑃(3)

=16 +

16

=13

35 Kelsey draws from a standard deck of cards. What is the chance she draws an Ace or a King?


=852

=213

36 Justify your previous solution using a probability rule.

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

𝑃(𝐴𝑐𝑒𝑜𝑟𝐾𝑖𝑛𝑔) = 𝑃(𝐴𝑐𝑒) + 𝑃(𝐾𝑖𝑛𝑔)

=452 +

452

=213

37


38 The Multiplicative Rule of Probability

“AND” is “TIMES”

39 Terry tosses a coin and throws a die. Show the sample space listing all of the possible outcomes.

If there are TWO events, use a TWO-Way Table! Die Coin

1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6

40 Use the Two-Way table from the previous question to work out the probability of rolling a Heads and getting a 3.


=112

41 Terry tosses two coins. Show the sample space listing all of the possible outcomes.

If there are TWO events, use a TWO-Way Table! Coin 1 Coin 2

H T H HH HT T TH TT

42 Use the Two-Way table from the previous question to work out the probability of rolling 2 heads.


=14


43 Barry tosses a coin and throws a die. Show the sample space listing all of the possible outcomes. ** Yes, draw ANOTHER 2-way table … its good practice**


1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6

44 Use the Two-Way table from the previous question to work out the probability of rolling a Tails and getting an odd number.


=312

=14

45 Use the same Two-Way table to work out the probability of rolling a Heads and getting and a number smaller than 3.


=212

=16

46 Terry tosses a coin and throws a die. Show the sample space listing all of the possible outcomes.


1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6

47 Terry tosses a coin and throws a die. How many different possible outcomes are there?

From the Two Way table… there are 12 possible outcomes. So;

𝑃𝑂 = 12


48 Terry tosses a coin and throws a die. What is the chance he tosses a Heads and rolls a 3?

Die Coin

1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6


=112

49 Terry tosses a coin and throws a die. What is the chance he tosses a Heads and rolls an even number?

Die Coin

1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6


=312

=14

50 Terry tosses a coin and throws a die. What is the chance he tosses a Heads and rolls a number bigger than 2?

Die Coin

1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6


=412

=13


51 Terry tosses a coin and throws a die. What is the chance he tosses a Tails and rolls a number at most 2?

Die Coin

1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6


=212

=16

52 Do I need to be able to draw a Two Way table? YES!

53 Two coins are tossed. Use a tree diagram to determine the probability of obtaining: (a) 2 Heads (b) 1 Head, then a Tail (c) one of each.

Answers:

(a) P(HH) =

(b) P(HT) =

P(HT or TH) =

P(HT or TH) =

14

14

2412


54 For breakfast, Ben has a choice between cereal and toast and a choice between milk and juice. Prepare a tree diagram to determine the probability of him having: (a) cereal and juice (b) toast and milk (c) juice

Answers:

(a) P(CJ) =

(b) P(TM) =

P(CJ or TJ) = =

55 There is a bag with 1 Blue and 2 Green balls in it. Show all of the possible outcomes if you select 2 balls successively. ** Successively means that you do not replace the first ball! When this happens, you need to do a Tree Diagram!

Refer Below

56

57 Use the tree diagram to determine the probability of drawing a Blue ball and then a Green ball.


=26

=13

141424

12

Green Blue GreenBlue

Green Blue Green

Blue Green Blue

Green

Green Green Green

Blue Green BlueGreen

Green Green Green


58 A married couple have 3 children. Construct a tree diagram showing all the different combinations of boys and girls the couple could have.

See below!

59

60 A married couple have 3 children. From your Tree Diagram, what is the probability they have 3 boys?


𝑃 =18

61 A married couple have 3 children. From your Tree Diagram, what is the probability that have a girl, followed by a boy, followed by a boy?


𝑃 =18

62 A married couple have 3 children. From your Tree Diagram, what is the probability that have two girls?


𝑃 =38


63 Not Needed in 2020 Are the following statements true or false? (a) The events of choosing a red card, or a

black card, from a deck of cards, are complementary events.

(b) The weather being sunny or cloudy are

complimentary events. (c) Selecting an odd or even number are

complementary events. (d) Having weather that is sunny or rainy are

complementary events. (e) Selecting vowels or consonants are

complimentary events. (f) Winning or losing are complementary

events (g) Are black and white complementary

events. (h) Being a dog, or a cat person are

complementary events (i) Like maths and not like maths are

complimentary events. (j) Cloudy or rainy weather are

complimentary events.

Answers: (a) True (b) False (there are many other types of

weather (c) True (d) False (it could also be cloudy or snowy or

windy etc)

(e) True

(f) False (you could come second, or not finish)

(g) False ( there are many other colours to

choose)

(h) False ( you could like salamanders?)

(i) True

(j) False (there are many other types of weather)

Documents

WorkSHEET 13.1 Probability Name: · WorkSHEET 13.1 Probability Name: _____ 1 Are the following statements true or false? (a) The events of choosing a red card, or a black card, from