EXAMPLE 3.4.8

A survey of Gators indicates that 7% are charming, 4% are modest, and 3% are both charming and modest. Find the probability that a Gator is modest, given that he/she is charming.

A. .75

B. .03

C. .43

D. .25

SOLUTION

Becuase the information is given in terms of percents, we can pretend that the total population is 100. In that case, the following Venn diagram summarizes the distribution.

Given that the Gator is charming, we know that it must be one of the 7 Gators in that circle:

Since 3 of the 7 charming Gators are modest, we have

P(modest, given charming) = 3/7 or roughly .43.