Question

In: Statistics and Probability

Suppose that it rains in Spain an average of once every 13 days, and when it...

Suppose that it rains in Spain an average of once every 13 days, and when it does, hurricanes have a 4% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 2% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford?

Solutions

Expert Solution

P(rains in Spain) = 1/13

P(hurricanes in Hartford | rains in Spain) = 0.04

P(hurricanes in Hartford | doesn't rain in Spain) = 0.02

P(hurricanes in Hartford) = P(hurricanes in Hartford | rains in Spain) * P(rains in Spain) + P(hurricanes in Hartford | doesn't rain in Spain) * P(doesn't rain in Spain)

                                        = 0.04 * 1/13 + 0.02 * (1 - 1/13)

                                        = 0.0215

P(rains in Spain | hurricanes in Hartford) = P(hurricanes in Hartford | rains in Spain) * P(rains in Spain) / P(hurricanes in Hartford)

                                                                 = 0.04 * 1/13 / 0.0215

                                                                 = 0.1431 (ans)

orchestra answered 2 years ago
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