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WHAT IS PROBABILITY? CLIL project Class II C. ACTIVITIES CLIL project Class II C.

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Presentation on theme: "WHAT IS PROBABILITY? CLIL project Class II C. ACTIVITIES CLIL project Class II C."— Presentation transcript:

1 WHAT IS PROBABILITY? CLIL project Class II C

2 ACTIVITIES CLIL project Class II C

3 likely probable coinoutcome sample space JackKing probability set event Gambing

4 CLASSICAL DEFINITIONFREQUENTIST DEFINITIONSUBJECTIVE PROBABILITY Bruno De Finetti proposed the subjective theory of Probability and he worked in Triest in the first half of the XX century (University, Assicurazioni Generali) favourable possible probabilitydivided favourableoutcomes cases 3/6 = 1/2 3/104/10 12/90 =6/45 2/5 X0 X 0 X1 X0 X0 X0 X1 X0 X1 X1

5 J A C K ASE ASE TOSSTOSSS N E F R E Q U N T I T P OBABILITY P OBABILITY F V O R A B L E D R A W LPLACE LPLACE FINETTI FINETTI L K E L Y H E D C R T A I N C O N ARD ARD Z E O

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

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8 EVENT AEVENT BID 1Rolling a die, number 3 is drawnRolling the same die, number 4 is drawn x 2Picking a card, its a king Picking a card from the same pack without replacement, its a jack 3Picking a card, its a king Picking a card from the same pack with replacement, its a four 4A man chosen randomly is a smokerA man chosen randomly is affected by heart diseases 5 One of you, chosen randomly, likes English One of you, chosen randomly, likes CLIL course 6Number 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 8Schumacher winsA Ferrari car wins 9Number 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 drawn 1/6 independent P = 1/6 1/6 = 1/36 LINE2: LINE3: LINE9: [in roulette there are 37 numbers] x x x x x x x x x 4/52 4/51 dependent P=4/52 4/51=16/2652 4/52 4/52 independent P=4/52 4/52=16/2704 1/37 1/37 independent P=1/37 1/37=1/1369

9 I N D I P E N D E N T N T E R S E C T I O N M U L I P L I C A T I O N O X C L U S I V E A D D T I O N MUTU LLYMUTU LLY A DV E N N D SJOITD SJOIT X X X X X X X X

10 III) Find the probability of the events formed by the following couples of disjoint events: Event A: Rolling a die, a 3 is drawn P(A) = _______ Event B: Rolling a die, a 5 is drawn P(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 club P(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 roulette P(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 0,45 Event B: the probability that tomorrow itll be snowy is 0,15 Which 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? 1/6 1/6 + 1/6 =2/6 1/4 1/4 + 1/4 =1/2 1/37 0/37 1/37 + 0/37 =1/37 7/90 9/90 7/90 + 9/90 =16/90 0,45+0,15 =0,60 6/14 5/14 6/14 + 5/14 =11/14

11 Name and Surname______________________________ ACTIVITY 6. TOTAL PROBABILITY and REVIEW I)Find the probability of the events formed by the following couples of not disjoint events: Event A: Rolling a die, a multiple of 2 is drawn P(A) = 3/6 Event B: Rolling a die, a multiple of 3 is drawn P(B) = 2/6 Event (A B): Rolling a die, a multiple of 2 and a multiple of 3 is drawn P (A B) = 1/6 Which is the probability of rolling a multiple of 2 OR a multiple of 3 on a die? P (A B)=3/6 + 2/6 – 1/6 = 4/6 Event A: Drawing a card its a heart P(A) = _______ Event B: Drawing a card its a faceP(B) = _______ Event (A B): Drawing a card, its a heart and a face P (A B) = _______ Which is the probability of drawing a heart OR a face from an ordinary deck? P (A B)= 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 (A B): Drawing a number, its a multiple of 12 OR a multiple of 10 P (A B) = _______ Which is the probability of drawing a multiple of 12 OR a multiple of 10? P (A B)= 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 (A B): Drawing a marble, its green and big P (A B) = _______ Which is the probability that a green OR a big marble is drawn? P (A B)= 13/52 12/52 3/52 13/52+12/52-3/52 7/90 9/90 1/90 7/90+9/90-1/90=15/90 14/25 11/25 6/25 14/25+11/25-6/25=19/25

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