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 ?

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%