A scientist sets up an experiment with Drosophila that requires her to make a measurement on each fly every day until all the flies are dead.

She knows that flies in her stock typically die at a rate of 3% per day, and she is willing to assume that probability of death is the same for each fly and is constant throughout its life. She is also willing to assume that the flies die independently of each other. She starts the experiment with 50 flies, 80 days before she plans to go on vacation.

a. What is the probability that an individual fly survives a given day?

b. What is the probability that an individual fly survives for 80 days?

c. What is the probability that the experiment will be finished (i.e., that all 50 flies will have died) before her vacation?

d. What is the probability that exactly two flies are left alive after 80 days?