a. 46.67%
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Use the formula for conditional probability:
- P(A|B) = P(A and B) / P(B)
From the given information, the probability of it being cloudy is 30% (0.3), and the probability of it being both cloudy and rainy is 14% (0.14).
Plugging these values into the formula:
- P(rainy|cloudy) = 0.14 / 0.3 ≈ 0.4667
Therefore, the probability of it being rainy, given that it will be cloudy, is approximately 46.67%.