In a simple model of the weather in October, each day is classified as either fine or rainy. The probability that a fine day is followed by a fine day is 0.8. The probability that a rainy day is followed by a fine day is 0.4 The probability that 1 October is fine is 0.75.

(a) Find the probability that 2 October is fine and the probability that 3 October is fine. answer: 0.7, 0.68

(b) Fine the conditional probability that 3 October is rainy, given that 1 October is fine. answer: 0.28

(c) Find the conditional probability that 1 October is fine, given that 3 October is rainy. answer: 0.65625

(C)