Question

Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.23 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded

Answer 1

14.72% probability that both professors get their grants funded

Explanation:

Independent events:

If two events, A and B are independent, the probability of both happening is:

`P(A \cap B) = P(A)*P(B)`

In this question:

Event A: Professor Jane is funded

Event B: Professor Joe is funded.

Professor Jane has a probability of 0.64 of being funded.

This means that
`P(A) = 0.64`

Professor Joe has probability 0.23 of being funded.

This means that
`P(B) = 0.23`

What is the probability that both professors get their grants funded

`P(A \cap B) = P(A)*P(B) = 0.64*0.23 = 0.1472`

14.72% probability that both professors get their grants funded