Question

You are off to a baseball game and want to be the catcher today, but that depends on the coach today. With Coach Smith, the probability of catching is 0.5 and with Coach Jones the probability of catching is 0.3. There is a 60% chance that Coach Smith will be there and a 40% chance that Coach Jones will be there. So, what is the probability that you will be catching today?

Answer 1

You have a 42% chance of catching today.

There are 2 situations in which you are going to catch.

Mr. Smith is the coach and he says yes. The probability of this happening is: 0.6 x 0.5 = 0.3

Mr. Jones is the coach and he says yes. The probability of this happening is: 0.4 x 0.3 = 0.12

If you add the probabilities together, you get 0.42 or 42%.