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

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.The respondent answered yes, given that the respondent was a female B.The respondent was a male, given that the respondent answered no 2.A coin is tossed 5 times. Find the probability of getting at least one tail. 3.Worksheet! GenderYesNo Male3218 Female842