Chapter 4.5, Problem 1E

Bayes’ Rule I A sample is selected from one of two populations, $S_1$and $S_2$, with $P\left(S_1\right)=.7$and $P\left(S_2\right)=.3$. Theprobabilities that an event A occurs, given that event 1 $S_1$and $S_2$has occurred are $P\left(A|S_1\right)=.2andP\left(A|S_2\right)=.3$
Use this information to answer the questions inExercises1−3.

1. Use the Law of Total Probability to find $P\left(A\right)$ .