Question

The probability for rain tomorrow is 3/5. If it rains tomorrow, the probability that john will practice his guitar is 3/5. If it does not rain tomorrow, the probability that john will practice his guitar is 3/10. What is the probability that john will practice his guitar tomorrow?

Answer 1

12/25

Explanation:

We can use the law of total probability to find the probability that John will practice his guitar tomorrow.

Let A be the event that it rains tomorrow, and let B be the event that John practices his guitar tomorrow. Then we have:

P(B) = P(A)P(B|A) + P(A^c)P(B|A^c)

Where A^c is the complement of A (i.e., the event that it does not rain tomorrow).

Substituting the given probabilities, we get:

P(B) = (3/5)(3/5) + (2/5)(3/10)

= 9/25 + 3/25

= 12/25

Therefore, the probability that John will practice his guitar tomorrow is 12/25.