Two professors are applying for grants Professor Jane has a

Two professors are applying for grants. Professor Jane has a probability of 0.68 of being funded. Professor Joe has probability 0.21 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?  
b. What is the probability that at least one of the professors will be funded?  
c. What is the probability that Professor Jane is funded but Professor Joe is not?  
d. Given at least one of the professors is funded, what is the probability that Professor Jane is funded but Professor Joe is not?

Solution

Since both the outcomes are independent,

a. What is the probability that both professors get their grants funded?  

= 0.68 * 0.21

= 0.1428
b. What is the probability that at least one of the professors will be funded?  

= 1 - P ( No professor is funded)

= 1 - [ ( 1 - 0.68 ) ( 1 - 0.21 )]

= 1 - 0.2528

= 0.7472
c. What is the probability that Professor Jane is funded but Professor Joe is not?  

= 0.68 * ( 1 - 0.21 )

= 0.68 * 0.79

= 0.5372
d. Given at least one of the professors is funded, what is the probability that Professor Jane is funded but Professor Joe is not?

= 0.5372 / 0.7472

= 0.7189

Hope this helps. Ask if you have doubts.