Math 120 SP08 SBrodnick
1
1
7.5
: Conditional Probability
& Independence
2
7.5: Conditional Probability & Independence
*
Entrées and desserts served at a charity event
that 250 people attended:
Prob. a person who had cheesecake had pork?
Rephrased:
Prob. a person had pork,
given that
he or she had cheesecake?
250
80
170
Total
150
45
105
Ice Cream (I)
100
35
65
Cheesecake (C)
Total
Beef (B)
Pork (R)
65/100
3
*
This is called
conditional probability
For this example, we write
P(R

C), where P(RC) =
=
=
*
In general, for events A and B (where P(B) ≠ 0)
P(AB) =
*
(back to table)
P(BI) =
P(CR) =
P(BC) =
P(R
∩
C)
P(C)
P(A
∩
B)
P(B)
65/250
100/250
65
100
“prob. of R
given
C”
7.5: Conditional Probability & Independence
45/150
65/170
35/100
4
*
A and B are
independent
if the outcome of one
does not affect the outcome of the other
*
Mathematically, P(A
∩
B) = P(A) · P(B)
(use this to test for independence)
Examples
:
1. Suppose P(E) = 0.7, P(F) = 0.8, and P(E
∩
F) = 0.6
Find P(EF) and P(FE).
2.Let A and B be independent events with
P(A) = 2/5 and P(B) = 3/4.
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 Spring '08
 Brodnick
 Math, Conditional Probability, Probability, Accountant, Probability theory

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