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Question

If it rains tomorrow, the probability is 0.8 that John will practice his cello. If it does not rain tomorrow, there is only a 0.4 chance that John will practice. Suppose the chance of tomorrow is 60%. What is the probability that John will practice his cello?

P(John will practice) =

Answer 1

P(John will practice | It rains) * P(It rains) + P(John will practice | It does not rain) * P(It does not rain)
P(John will practice) = 0.8 * 0.6 + 0.4 * 0.4
P(John will practice) = 0.48 + 0.16
P(John will practice) = 0.64

Therefore, the probability that John will practice his cello is 0.64.