Josiah has a 20% experimental probability of hitting the snooze button any morning when his alarm goes off. When he hits the snooze button there is a 25% conditional probability that he missed the bus. He has never missed the bus when he has not hit the snooze button. If Josiah's alarm woke him 120 times over the course of the semester, how many times did Josiah miss his bus?

6 times

Step-by-step explanation:

There are two events here:

1. Probability to hit snooze button = P (A) = 20%. Also mean P (A') = 80%

2. The probability to miss the bus = B

If Josiah hits the snooze button (A is happen), he misses the bus (B) 25% of the time. It mean P (B | A) = 25%

If Josiah doesn't hit the snooze button (A didn't happen), he won't miss the bus. It mean P (B | A') = 0%

If alarm woke Josiah 120 times, expected times that Josiah miss the bus will be:

P (B | A) * 120 * P (A) + P (B | A') * 120 * P (A') = 25%*20%*120 + 0% * 75%*120 = 6 times