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WHAT IS PROBABILITY? CLIL project Class II C

# WHAT IS PROBABILITY?

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WHAT IS PROBABILITY?. CLIL project Class II C. ACTIVITIES. CLIL project Class II C. likely. probable. coin. outcome. sample space. Jack. King. probability. set. event. Gambing. CLASSICAL DEFINITION. FREQUENTIST DEFINITION. SUBJECTIVE PROBABILITY. - PowerPoint PPT Presentation

### Text of WHAT IS PROBABILITY?

• WHAT IS PROBABILITY?CLIL projectClass II C

• ACTIVITIESCLIL projectClass II C

• likelyprobablecoinoutcomesample spaceJackKingprobabilityseteventGambing

KEY WORDS

1. The Puzzle

Find the words and eliminate the corresponding letters from the puzzle. The remaining letters form the name of the French mathematician who first proposed the classical definition of probability.

Car

Die

Jack

Outcome

Probable

Set

Card

Drawing

King

Pascal

rolling

Test

Case

Events

Likely

Pick

Sample space

Toss

Coin

Gambling

Occur

Probability

School

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2. Connect an English word with its Italian translation

Card

SCEGLIERE A CASO

Coin

Die

GIOCO DAZZARDO

to Draw

RISULTATO

Event

Gambling

CAPITARE

Jack

EVENTO

King

SPAZIO CAMPIONARIO

Likely

PROVARE

to OCCUR

CARTA DA GIOCO

Outcome

GETTARE (la moneta)

to Pick

PROBABILIT

Probability

INSIEME

to roll

RE

Sample space

PRENDERE

Set

MONETA

Test

PROBABILE

to Toss

FANTE

3. Put in the spaces the correct words from the list of key words.

a) The word _____________, ____________, and hazardous are synonyms.

b) Tossing a ___________ I got head. Head is the _____________ of my experiment.

c) All the possible outcomes that can occur when I execute the experiment form the ______________.

d) The _________, the Queen and the ____________ are three cards of a pack.

e) The measure of how likely an event is, is called ________________.

f) The particular outcome or __________ of outcomes we are interested in, is an _________.

g) ____________ is dangerous for our pocket!

• CLASSICAL DEFINITIONFREQUENTIST DEFINITIONSUBJECTIVE PROBABILITYBruno De Finetti proposed the subjective theory of Probability and he worked in Triest in the first half of the XX century (University, Assicurazioni Generali)favourablepossibleprobabilitydividedfavourableoutcomescases3/6 = 1/23/10 4/10 12/90 =6/45 2/5X0X0X1X0X0X0X1X0X1X1

Name and Surname ___________________

ACTIVITY 2: PROBABILITY

1. There are three possible ways to find probability:

LACISCASL EINFTIDON, QFIUSTTNEERU EFDOTNINI, ECJTIUVBSE IBLIARTBYOP.

__________ __________, ___________ ___________, _____________ ___________.

2. Write a phrase about Bruno De Finetti.

______________________________________________________________________

______________________________________________________________________

3. Complete the formula for the classical definition of Probability:

Probability Of An Event P(A) = The Number of __________________cases

The number of

cases

4. The ________________ of event A is the number of ways event A can occur ___________ by the total number of possible ___________. The probability of event A is the number of ____________ cases (outcomes) divided by the total number of possible ______________ (outcomes).

cases

divided

favourable

outcomes

probability

5. Exercises:

a) What is the probability of rolling an even number with a die?

b) In a bag we have 10 pens: 3 green, 4 red and the remaining blue. Picking a pen up, what is the probability of picking a green one? What is the probability for a red one?

c) Playing Tombola, what is the probability of drawing a multiple of 7?

d) In a box we have 5 candles, three used and two new ones. What is the probability of drawing a new one from the box?

6. Which of the following events are certain and which impossible? In the last column, write the appropriate probability (zero or one).

What is the probability that

EVENT

certain

impossible

P(A)

rolling a die, a number greater than 8 is drawn?

in a this year Formula 1 race, Alex Del Piero wins?

playing tombola, a number less than 100 is drawn?

in the today Mathematics test, Lisa receives 12 (shes is very good, indeed!)?

Giovanni works in Nolandia (?)?

rolling two dice, the sum of the numbers is 20?

choosing a letter from the alphabet, its a consonant or a vowel.

picking a card up from an ordinary pack, its a 15 of clubs.

choosing a boy among your schoolmates, he is a Carducci student?

this morning you dont meet a Lunar girl?

• J A C K ASETOSSN E F R E Q U N T I T P OBABI LI TY F V O R A B L E D R A W L

P LACE

F INE TTIL K E L YH E D C R T A I NC O N ARD Z E O

ACTIVITY 3

Crossword: the Theory of probability

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Across:

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It's a card with the image of a soldier

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The probability of a certain event

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The probability definition which involves frequency

8

In Italian it's: scegliere a caso

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In the Laplace's formula, these are the cases at the numerator

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Synonym of probable

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In the coin, it's the opposite of tail

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An event which has P(A)=1

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The object I toss

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The probability of an impossible event

Down:

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In Italiano it's "caso"

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The verb for a coin

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The measure of how probable an event is

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The "De", famous French mathematician

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Famous Italian mathematician who proposed the subjective theory of probability

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A jack is a .....

EXERCISES

1. In a sack we have three blue little balls, two white balls and four yellow balls. Which is the probability of drawing a blue ball from the sack? Which is the probability of drawing any ball except a blue one? (use complement definition)

2. In an ordinary pack (for briscola) there are 40 cards. Four of those are jacks. Drawing a card, which is the probability of getting a jack? Which is the probability of drawing any card, except a jack? (use complement definition)

3. Which is the probability of drawing from the sack a Tombola number bigger than 75? Which is the probability of drawing a number less or equal to 75? (use complement definition).

4. Rolling a die, which is the probability of rolling an odd number? And which is the probability of rolling an even number? (use complement definition)

5. Im thinking about a day of the year. Which is the probability that it is exactly your birthday? Which is the probability that isnt your birthday? (use complement definition).

6. Three pens are good and five are not. Drawing one pen of the set, which is the probability of drawing a good pen? Which is the probability of getting a bad one? (use complement definition).

7. If I have a probability equal to 0,23 to complete this activity in half an hour, which is the probability that I will not complete it in half an hour? (use complement definition).

8. A party has a probability P(A)=0,73 of winning the elections. Which is the probability that this party loses? (use complement definition).

9. Which is the probability of rolling a 7 with an ordinary die? Which is the probability of rolling any number except a 7? (use complement definition).

• P(blue)=3/9=1/3 P(not blue)= 1 1/3=2/3P(jack)=4/40=1/10 P(not jack)= 1 1/10=9/10P(>75)=15/90=1/6 P(not >75)= 1 1/6=5/6P(odd)=3/6=1/2 P(even: not odd)= 1 1/2=1/2P (your birthday)=1/365 P(not your birthday)= 1 1/365=364/365P(good)=3/8 P(bad: not good)= 1 3/8=5/8P(I complete)=0,23 P(I dont complete)= 1 0,23 = 0,77P(wins)=0,73 P(loses: doesnt win)= 1 0,73 = 0,27P(7)=0 P(not 7)= 1 0 = 1

EXERCISES

1. In a sack we have three blue little balls, two white balls and four yellow balls. Which is the probability of drawing a blue ball from the sack? Which is the probability of drawing any ball except a blue one? (use complement definition)

2. In an ordinary pack (for briscola) there are 40 cards. Four of those are jacks. Drawing a card, which is the probability of getting a jack? Which is the probability of drawing any card, except a jack? (use complement definition)

3. Which is the probability of drawing from the sack a Tombola number bigger than 75? Which is the probability of drawing a number less or equal to 75? (use complement definition).

4. Rolling a die, which is the probability of rolling an odd number? And which is the probability of rolling an even number? (use complement definition)

5. Im thinking about a day of the year. Which is the probability that it is exactly your birthday? Which is the probability that isnt your birthday? (use complement definition).

6. Three pens are good and five are not. Drawing one pen of the set, which is the probability of drawing a good pen? Which is the probability of getting a bad one? (use complement definition).

7. If I have a probability equal to 0,23 to complete this activity in half an hour, which is the probability that I will not complete it in half an hour? (use complement definition).

8. A party has a probability P(A)=0,73 of winning the elections. Which is the probability that this party loses? (use complement definition).

9. Which is the probability of rolling a 7 with an ordinary die? Which is the probability of rolling any number except a 7? (use complement definition).

• Name and Surname______________________________

ACTIVITY 4. COMPOUND EVENT

I) Answer to the following questions:

a) Which is the key conjunction in the compound event?

1) OR

(

2) AND

(

3) BECAUSE

(

4) THAT

(

b) When two events are independent?

1) When they are logically connected.

(

2) When the fact that A occurs affects the probability of B occurring.

(

3) When one follows the other.

(

4) When the fact that A occurs does not affect the probability of B occurring.(

c) Which is the arithmetical operation for the calculation of a compound event?

1) Subtraction

(

(

3) Division

(

4) Multiplication

(

d) In Theory of probability the symbol P(B | A) means that

1) the probability of event B must be divided by the probability of event A

(

2) the probability of event B is influenced by the fact that event A has occurred

(

3) the probability of event B must be divided by the probability of event A

(

4) the probability of event B is not influenced by the fact that event A has occurred(

e) If you draw a coloured ball from a sack (event A) and then you draw another one (event B), the two events:

are always independent

(

are never independent

(

are independent only if we put back (replace) the first ball in the sack

(

are independent only if we dont put back (replace) the first ball in the sack(

II) In the table we have nine couples of events (event A; event B). Indicate the couples of dependent (D) events and of independent events (I)

EVENT A

EVENT B

I

D

1

Rolling a die, number 3 is drawn

Rolling the same die, number 4 is drawn

x

2

Picking a card, its a king

Picking a card from the same pack without replacement, its a jack

3

Picking a card, its a king

Picking a card from the same pack with replacement, its a four

4

A man chosen randomly is a smoker

A man chosen randomly is affected by heart diseases

5

One of you, chosen randomly, likes English

One of you, chosen randomly, likes CLIL course

6

Number 37 is drawn, playing Tombola.

Number 43 is drawn, playing Tombola

7

Schumacher wins the next F1 Championship

Juventus wins 2005-2006 Italian football championship

8

Schumacher wins

A Ferrari car wins

9

Number 18 is drawn at roulette

Number 12 is drawn at roulette

III) Calculate the probabilities of the compound events formed by the two events on a line in the table (lines: 1,2,3,9) (look at the example of line 1)

P(A)

P(B)

dependent/independent

P(compound event)

LINE1: EVENT A: rolling a die, number 3 is drawn; EVENT B Rolling the same die, number 4 is drawn

1/6

1/6

independent

P = 1/6 ( 1/6 = 1/36

LINE2:

LINE3:

LINE9: [in roulette there are 37 numbers]

• xxxxxxxxx4/52 4/51 dependent P=4/52 4/51=16/26524/52 4/52 independent P=4/52 4/52=16/27041/37 1/37 independent P=1/37 1/37=1/1369

EVENT AEVENT BID1Rolling a die, number 3 is drawnRolling the same die, number 4 is drawnx2Picking a card, its a kingPicking a card from the same pack without replacement, its a jack3Picking a card, its a kingPicking a card from the same pack with replacement, its a four4A man chosen randomly is a smokerA man chosen randomly is affected by heart diseases5One of you, chosen randomly, likes EnglishOne of you, chosen randomly, likes CLIL course6Number 37 is drawn, playing Tombola.Number 43 is drawn, playing Tombola7Schumacher wins the next F1 ChampionshipJuventus wins 2005-2006 Italian football championship8Schumacher winsA Ferrari car wins9Number 18 is drawn at rouletteNumber 12 is drawn at roulette

P(A)P(B)dependent/independentP(compound event)LINE1: EVENT A: rolling a die, number 3 is drawn; EVENT B Rolling the same die, number 4 is drawn1/61/6independentP = 1/6 1/6 = 1/36LINE2:

LINE3:

LINE9: [in roulette there are 37 numbers]

II) In the table we have nine couples of events (event A; event B). Indicate the couples of dependent (D) events and of independent events (I)

III) Calculate the probabilities of the compound events formed by the two events on a line in the table (lines: 1,2,3,9) (look at the example of line 1)

• I N D I P E N D E N T NTERSEC T ION M U L I P L I C A T I O NOX C L U S I V EA D D T I O NMU TU L L YA DV E N ND SJOI

TXXXXXXXX

Name and Surname______________________________

ACTIVITY 5. MUTUALLY EXCLUSIVE EVENTS

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Crossword

Across:

1. Two events, A and B, are _____ if the fact that A occurs does not affect the probability of B occurring.

2. The "rule" for compound event.

3. The "key" conjunction for two independent events when I ask that one of them occurs

6. Two events are mutually ____ if it is impossible for them to occur together.

7. The "rule" for finding the probability in the "OR" case.

8. The "key" conjunction for the compound event

9. ____s diagrams show the sets we are studying

Down:

1. The operation between sets which involves the compound event. Its symbol is (.

4. Two events are _________ exclusive , if it is impossible for them to occur together.

5. We say "mutually exclusive" events or _______ events

II) In the table we have nine couples of events (event A; event B). Indicate the couples of mutually exclusive (disjoint D) events and of not mutually exclusive (NME)

EVENT A

EVENT B

ME

NME

1

Number 32 is drawn, playing Tombola

Number 87 is drawn, playing Tombola

x

2

Rolling a die, a 3 is drawn

Rolling a die, a 4 is drawn

3

Drawing a cards its a club

Drawing a card, its a king

4

Schumacher wins

Alonso wins

5

Schumacher wins

A Ferrari car wins

6

Choosing randomly a letter, its a vowel

Choosing randomly a letter, its a consonant

7

Rolling a die an odd number is drawn

Rolling a die a multiple of 3 is drawn

8

Choosing randomly a day, its in March

Choosing randomly a date, its an odd number

9

Choosing randomly a song, its sung in English

Choosing randomly a song, its sung by an American singer

• III) Find the probability of the events formed by the following couples of disjoint events:

1/61/61/6 + 1/6 =2/6 1/41/41/4 + 1/4 =1/2 1/37 0/371/37 + 0/37 =1/37 7/909/907/90 + 9/90 =16/90 0,45+0,15 =0,60 6/145/146/14 + 5/14 =11/14

Event A: Rolling a die, a 3 is drawn P(A) = _______Event B: Rolling a die, a 5 is drawnP(B) = _______Which is the probability of rolling a 3 OR a 5 on a die? Event A: Drawing a card its a spade P(A) = _______Event B: Drawing a card its a clubP(B) = _______Which is the probability of drawing a spade OR a club from an ordinary deck?Event A: Getting number 31 at the roulette P(A) = _______Event B: Getting number 37 at the rouletteP(B) = _______Which is the probability of getting a 31 OR a 37 at the roulette?Event A: Drawing a Tombola number, its a multiple of 13 P(A) = _______Event B: Drawing a Tombola number, its a multiple of 9P(B) = _______Which is the probability of drawing a multiple of 13 OR a multiple of 9?Event A: the probability that tomorrow itll be cloudy is 0,45Event B: the probability that tomorrow itll be snowy is 0,15Which is the probability that tomorrow it will be cloudy OR snowy?In a jar there are 14 coloured marbles: 6 green, 3 red, 5 blue ones.Event A: A green marble is drawn P(A) = _______Event B: A blue marble is drawn P(B) = _______Which is the probability that a green OR a blue marble is drawn?

• Name and Surname______________________________

ACTIVITY 6. TOTAL PROBABILITY and REVIEW

Find the probability of the events formed by the following couples of not disjoint events:

13/5212/523/5213/52+12/52-3/527/909/901/907/90+9/90-1/90=15/9014/2511/256/2514/25+11/25-6/25=19/25

Event A: Rolling a die, a multiple of 2 is drawn P(A) = 3/6Event B: Rolling a die, a multiple of 3 is drawn P(B) = 2/6Event (AB): Rolling a die, a multiple of 2 and a multiple of 3 is drawn P (AB) = 1/6Which is the probability of rolling a multiple of 2 OR a multiple of 3 on a die?P (AB)=3/6 + 2/6 1/6 = 4/6Event A: Drawing a card its a heart P(A) = _______Event B: Drawing a card its a faceP(B) = _______Event (AB): Drawing a card, its a heart and a face P (AB) = _______Which is the probability of drawing a heart OR a face from an ordinary deck? P (AB)=Event A: Drawing a Tombola number, its a multiple of 12 P(A) = _______Event B: Drawing a Tombola number, its a multiple of 10 P(B) = _______ Event (AB): Drawing a number, its a multiple of 12 OR a multiple of 10 P (AB) = _______Which is the probability of drawing a multiple of 12 OR a multiple of 10?P (AB)=In a jar there are 25 coloured marbles: 6 green and big, 8 green and small, 5 blue and big, 6 blue and small.Event A: A green marble is drawn P(A) = _______Event B: A big marble is drawn P(B) = _______ Event (AB): Drawing a marble, its green and big P (AB) = _______Which is the probability that a green OR a big marble is drawn? P (AB)=

• II) Solve the following exercises (repetition):

1. What is the probability that choosing randomly among the students of your own class for a test, the chosen student is exactly you?

2. What is the probability that in this year Formula 1 race, Alex Del Piero wins?

3. What is the probability that choosing a boy among your schoolmates, he is a Carducci student?

4. In a sack we have three blue little balls, two white balls and four yellow balls. Which is the probability of drawing a blue ball from the sack? Which is the probability of drawing any ball except a blue one? (use complement definition)

5. Im thinking about a day of the year. Which is the probability that it is exactly your birthday? Which is the probability that isnt your birthday? (use complement definition).

6. What is the probability that, picking a card, its a king and afterwards, picking another card from the same deck with replacement, its a four?

7. Playing Tombola number 33 is drawn and, afterwards, number 12 is drawn. Which is the probability of this compound event?

8. Which is the probability of rolling a 3 OR a 5 on a die?

9. If the probability that tomorrow itll be cloudy is 0,45 and the probability that tomorrow itll be snowy is 0,15, which is the probability that tomorrow it will be cloudy or snowy?

10. Playing Tombola, which is the probability of drawing a multiple of 12 or a multiple of 10?

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