In Cook County each day is either sunny or cloudy If a day i

In Cook County, each day is either sunny or cloudy. If a day is sunny, the following day will be sunny with probability 0.60. If a day is cloudy, the following day will be cloudy with probability 0.70. Suppose it is cloudy on Monday. Show Work

(a) What is the probability that it will be sunny on Tuesday?

(b)What is the probability that it will be sunny on both Tuesday and Wednesday?

(c) What is the probability that it will be sunny on Wednesday?

Solution

a) Given Monday is cloudy. so P( tuesday is sunny ) = 1-0.70 = 0.30

b) Given monday is cloudy, P(both tuesday and wednesday is sunny) = P(tuesday is sunny) * P(wednesday is sunny given tuesday is sunny) = 0.30 * 0.60 = 0.18

c) P(wednesday sunny) = P(wednesday sunny given tuesday sunny) + P(wednesday sunny given tuesday cloudy)

= 0.6 + 0.3 = 0.9