Question

Assume that E and F are independent events. Use the given information to find

Pr(F). Pr(E)equals=0.70.7 and Pr(F|E)equals=0.50.5

Find: Pr(F)

Answer 1

P(F)=0.50

Explanation:

Given : Assume that E and F are independent events.

`P(E)\cdot P(F)=0.70` and
`P(F/E)=0.50`

To find : Probability of F?

Solution :

When E and F are independents then,

`P(E\cap F)=P(E)\cdot P(F)`

The conditional probability of independent events is

`P(F/E)=(P(E\cap F))/(P(E))`

Substitute,

`P(F/E)=(P(E)\cdot P(F))/(P(E))`

`P(F/E)=P(F)`

Which means
`P(F/E)=0.50=P(F)`

Therefore, Probability of F is P(F)=0.50.