Aim: How do we find the
conditional probability of an event?
TEST TUESDAY
Conditional Probability
• The conditional probability of an event B in
relationship to event A was defined as the
probability that event B occurs after event A
has already occurred
• The conditional probability of an event can be
found by dividing both sides of the equation
for the multiplication rule 2 by P(A)
What is conditional probability?
• conditional probability: the probability of one event
occurring under the condition that we know the
outcome of another event
• Let A and B be two events in a sample space, with P(A)
> 0. The conditional probability of event B, given that A
has occurred,(written P(B|A)) is
• P(B|A) read as “probability of B, given A” has happened
or probability of B if A is true.
• Note that if A and B are independent, P(B|A) = P(B)
Example
• Are boys more likely to have sisters than
brothers?
– Let S be possible outcomes for a two child family
• B = event {at least one child is a boy},
• A = event {at least one child is a girl}
Example
• A box contains black chips and white chips. A person
selects two chips without replacement. If the
probability of selecting a black chip and a white chip is
15/56, and the probability of selecting a black chip on
the first draw is 3/8, find the probability of selecting
the white chip on the second draw, given that the first
chip selected was a black chip.
• Solution: B = selecting back W = selecting white
15
P( B & W ) 56 5
P(W | B) 


3 7
P( B)
8
Summary: Conditional Probability
Class Work
1.
A recent survey asked 100 people if they thought women in the
armed forces should be permitted to participate in combat. The
results of the survey are shown. Find the probabilities of:
A.
B.
2.
3.
The respondent answered yes, given that the respondent was a
female
The respondent was a male, given that the respondent answered no
Gender
Yes
No
Male
32
18
Female
8
42
A coin is tossed 5 times. Find the probability of getting at least one
tail.
Worksheet!