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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

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

outcomes

favourable

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

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

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 don’t complete)= 1 – 0,23 = 0,77

P(wins)=0,73 P(loses: doesn’t win)= 1 – 0,73 = 0,27

P(7)=0 P(not 7)= 1 – 0 = 1

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

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

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

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

0,45+0,15 =0,60

6/14

5/14

6/14 + 5/14 =11/14

- Name and Surname______________________________
- ACTIVITY 6. TOTAL PROBABILITY and REVIEW
- Find the probability of the events formed by the following couples of not disjoint events:

13/52

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