1. In a well known quiz show, the contestant is asked to choose between door number 1, door number 2, and door number 3. The grand prize, of course, is behind one of the doors. Suppose that each of the next 8 individuals that play this game intend to choose "their door" randomly.
a) Find the probability that
a. Exactly 4 will win the grand prize,
b. Between 3 and 5 inclusive will win the grand prize
b) Find:
a. The mean (expected) number of grand prize winners,
b. The variance and standard deviation
2. A sailor monitoring radar on board a U.S. warship has a 0.90 probability of correctly identifying the type of aircraft from information on the radar screen. Consider the next 14 identifications made by the sailor.
a) Find the probability that he makes
a. At least 10 correct identifications,
b. Between 9 and 12 correct identifications (inclusive),
c. No incorrect identifications
b) Find the mean (expected) number of correct identifications
c) Find the variance and standard deviation