Two professors are applying for grants. Professor Jane has a probability of 0.65 of being funded. Professor Joe has probability 0.24 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent.
a.) What is the probability that both professors get their grants funded? Give your answer to four decimal places.
b.) What is the probability that at least one of the professors will be funded? Give your answer to four decimal places.
c.) What is the probability that Professor Jane is funded but Professor Joe is not? Give your answer to four decimal places.
d.) Given at least one of the professors is funded, what is the probability that Professor Jane is funded but Professor Joe is not? Give your answer to four decimal places.