If it rains ​tomorrow, the probability is 0.6 that John will practice his guitar. If it does not rain ​tomorrow, there is only a 0.3 chance that John will practice.

Question

If it rains ​tomorrow, the probability is 0.6 that John will practice his guitar. If it does not rain ​tomorrow, there is only a 0.3 chance that John will practice. Suppose the chance of rain tomorrow is 60​%. What is the probability that John will practice his guitar​?

Answer 1

If there's a 60% chance of rain and 60% chance he practices when it rains, then we can reword this to say that his odds of practicing tomorrow are "60% of 60% and 30% of 40%". so .6 * .6 + .3 * .4 = .48 = 48 percent chance