Question

The weatherman predicts a 20% chance of rain on Thursday. If it rains, there is a 10% chance that your roof will leak. (If it doesn't rain, of course, your roof is safe.) What is the chance that you will have a leaky roof on Thursday

Answer 1

2%

Explanation:

Probability of rain, P(R) = 0.2

Probability of leak Given that it rains, P(L|R) = 0.1

Probability of leak Given that it does not rain, P(L|R') = 0

According to Baye's Rule:

P(L) = [P(L|R) * P(R)] + [P(L|R') * P(R')]

P(R') = 1 - P(R) = 1 - 0.2 = 0.8

P(L) = [0.1 * 0.2] + [0 * 0.8]

P(L) = 0.02 + 0

P(L) = 0.02

Hence, probability of a roof leak on Thursday is 0.02 = (0.02 * 100%) = 2%