Question

Suppose that e and f are events in a sample space and p(e) = 2/3, p(f) = 3/4, and p(f |

e.= 5/8. find p(e | f).

Answer 1

Using the definition of conditional probability, we have


`\mathbb P(E\mid F)=(\mathbb P(E\cap F))/(\mathbb P(F))=(\mathbb P(F\mid E)\cdot\mathbb P(E))/(\mathbb P(F))`

so the probability we want is


`(\frac58\cdot\frac23)/(\frac34)=\frac59`