Question

If it rains ​tomorrow, the probability is 0.6 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 rain tomorrow is 70​%.
What is the probability that John will practice his cello​?

Answer 1

The final probability is the weighted average of the playing probabilities calculated over the possible weather options:

P(john practices cello; given that it rains) * P(it rains) +

P(john practices cello; given that it does not rain) * P(it does not rain) =

0.6 * 0.7 + 0.4 * 0.3 = 0.54

The probability is 54%