Note that in this case we need to use conditional probability. The expression P(B|A) means the probability of event B occurring given that event A has occurred.
5574, or about 74.3 %
Practice makes perfect
We are told that at a shoe store yesterday 74 % of customers bought shoes, 38 % bought accessories, and 55 % bought both shoes and accessories. We want to find the probability of randomly selecting a customer who bought accessories given that they bought shoes. Note that in this case we need to use conditional probability.
P(B|A)=P(AandB)/P(A)
The expression P(B|A) means the probability of event B occurring given that event A has occurred. In our case event B will be buying accessories by a customer, which we will mark as A. Event A will be buying shoes, which we will mark as S.
P( A| S)=P( S and A)/P( S)
We know that 55 % of customers bought both shoes and accessories, so the probability that a customer who bought both items is selected is 55 %= 0.55. Also, 74 % of customers bought shoes. This means that the probability of selecting a customer who bought shoes is 74 %= 0.74.
P(SandA)=& 0.55
P(S)=& 0.74
Let's substitute these values into our expression and find the conditional probability!
