Question

At a busy city intersection the probability is 0.08 that an accident will occur on any...

At a busy city intersection the probability is 0.08 that an accident will occur on any given day.
However, if it rains that day, then the probability of an accident is 0.24. Weather records show that it
rains about 10 percent of the days in this city. Suppose you read in the paper that an accident did
occur at the intersection yesterday. Knowing this, what is the probability that it rained yesterday?

Math   Statistics-And-Probability   
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Answer #1

P(accident will occur) = 0.08

P(accident | rains that day) = 0.24

P(rains) = 0.1

P(rain | accident) = P(accident | rains that day) * P(rains) / P(accident will occur)

                            = 0.24 * 0.1 / 0.08

                            = 0.3

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