WHAT IS PROBABILITY?

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WHAT IS PROBABILITY?

• CLIL project
• Class II C

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ACTIVITIES

• CLIL project
• Class II C

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likely
probable
coin
outcome
sample space
Jack
King
probability
set
event
Gambing
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CLASSICAL DEFINITION
FREQUENTIST DEFINITION
SUBJECTIVE 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
probability
divided
favourable
outcomes
cases
3/6 1/2
3/10
4/10
12/90 6/45
2/5
X
0
X
0
X
1
X
0
X
0
X
0
X
1
X
0
X
1
X
1
5
J A C K
A SE
TO SS
N E
P OBABI LI TY
F R E Q U N T I T
L P L ACE
D R A W
F V O R A B L E
F I NE TT I
L K E L Y
H E D
C R T A I N
C O N
AR D
Z E O
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P(blue)3/91/3 P(not blue) 1 1/32/3
P(jack)4/401/10 P(not jack) 1 1/109/10
P(gt75)15/901/6 P(not gt75) 1 1/65/6
P(odd)3/61/2 P(even not odd) 1 1/21/2
P (your birthday)1/365 P(not your birthday) 1
1/365364/365
P(good)3/8 P(bad not good) 1 3/85/8
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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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
x
x
x
x
x
x
x
x
x
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 LINE1 EVENT A rolling a die, number 3 is drawn EVENT B Rolling the same die, number 4 is drawn LINE1 EVENT A rolling a die, number 3 is drawn EVENT B Rolling the same die, number 4 is drawn 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 LINE2 LINE2 LINE2

LINE3 LINE3 LINE3 LINE3

LINE9 in roulette there are 37 numbers LINE9 in roulette there are 37 numbers LINE9 in roulette there are 37 numbers LINE9 in roulette there are 37 numbers

4/52 4/51 dependent
P4/52 ? 4/5116/2652
4/52 4/52 independent
P4/52 ? 4/5216/2704
1/37 1/37 independent
P1/37 ? 1/371/1369
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N T ER SE C T I ON
I N D I P E N D E N T
M U L I P L I C A T I O N
O
M U T U L L Y
D S JO I T
X C L U S I V E
A D D T I O N
A D
V E N N
X
X
X
X
X
X
X
X
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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 9 P(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 1/6 2/6
1/4
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
0,450,15 0,60
6/14
5/14
6/14 5/14 11/14
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• Name and Surname_____________________________
  _
• ACTIVITY 6. TOTAL PROBABILITY and REVIEW
• 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 face P(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
13/5212/52-3/52
7/90
9/90
1/90
7/909/90-1/9015/90
14/25
11/25
6/25
14/2511/25-6/2519/25
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