An old car is never garaged at night. On the 1 morning following a wet night, the probability that the car does not start is. On the morning following a dry night, this probability is. The starting performance of the car each morning is independent of its performance on previous mornings.

(a) There are six consecutive wet nights. Determine the probability that the ear docs not start on at least two of the six mornings.

(b) During a wet autumn there are 32 wet nights. Using a suitable approximation, determine the probability that the car does not start on fewer than 16 of the 32 mornings.

(c) During a long summer drought there are 100 dry nights. Using a Poisson approximation, determine the probability that the car does not start on five or more of the 100 mornings. (Give three decimal places in your answers.) (C)