During a period of unsettled weather let a be the event of

Question

Question: During a period of unsettled weather, let A be the event of rain in Austin, B be the event of rain in Houston, and C be the event of rain in San Antonio. Suppose:

P(AB) = 0.35, P(AB^c) = 0.15,

P(AC) = 0.20, P(AB^c U A^cB) = 0.45

P(BC) = 0.30, P(B^cC) = 0.05 P(A^cB^cC^c) = 0.15

a. What is the probability of rain in all three cities?

b. What is the probability of rain in exactly two of the three cities?

c. What is the probability of rain in exactly one of the cities?