Two professors are applying for grants. Professor Jane has a probability of 0.61 of being funded. Professor Joe has probability 0.27 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? Give your answer to four decimal places

0.1647

Step-by-step explanation:

From the multiplication rule, we know that if two events are independent (which is the case here), then P (A and B) = P (A) * P (B)

Let P (A) be the probability of Professor Jane being approved, thus P (A) = 0.61

Let P (B) be the probability of Professor Joe being approved, thus P (B) = 0.27

The probability of both their grants being funded would be P (A and B), since it would be the intersection between these two events.

Thus, calculating: P (A and B) = 0.61*0.27=0.1647