Computing Probabilities
Sept. 08
Probability
A probability measure is a function from the
set of events to [0,1].
e.g. Roll 2 dice and record sum X
Prob(X=10)
Prob(X>10)
Prob(X=10 or X<3)
Probability – Formal Definition
A probability measure is a function from the set of
events to [0,1]:
1) P(A) ≥0
2) P(S)=1
3) If A
1
, A
2
,... is a finite or countable set of events
and A
i
∩
A
j
= Ø for all pairs
P(A
1
U A
2
U ... U A
n
) = P(A
1
)+ P(A
2
)+...+ P(A
n
)
P(A
1
U A
2
U ...) = P(A
1
)+ P(A
2
)+...
Basic Theorems
Theorems:
1) P(A)=1P(A’)
2) P(Ø)=0
3) If
then P(A)≤P(B)
4) P(A) ≤ 1
5) P(A U B)=P(A)+P(B)P(AB)
B
A
⊂
30% of the members of a fitness club are women.
40% of the members are doctors. 20% of the
members are male doctors.
If a member is selected at random (e.g. to complete a
survey on customer satisfaction) what is the
probability that the selected member is either a
woman or a doctor?
Basic Theorems
Theorems:
1) P(A)=1P(A’)
2) P(Ø)=0
3) If
then P(A)≤P(B)
4) P(A) ≤ 1
5) P(A U B)=P(A)+P(B)P(AB)
Consider theorem 3.
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 Fall '07
 SENTURK,DAMLA
 Probability, Probability theory, Simple random sample, Natural number

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