# Probability Homerun Problem

1. Apr 8, 2012

### mathmajor23

For this problem, make the assumption that each day is 10 hours long, and that all 7 days of every week you expect the same number of players to be playing all day long.

At the Country Club, players hit a homerun at an average rate of 5 per day.

1) What is the probability that the first ball to get hit for a homerun occurs during the 5th hour of the day?

2) What is the probability that the third ball to get hit for a homerun occurs during the 5th hour of the day? Express your answer as a function of the number e.

3) What is the probability that there are two days in a week where no balls get hit for a homerun?

My attempt:

1) Let X = time the first ball gets hit for a homerun ~ exp(mean 2 hours)
P(4<X<5) =

2) Let Y = time until third balls gets hit for a homerun ~ Gamma(3,2) hours
P(4<Y<5) = ... (not sure how to express answer as a function of e)

3) Let Z = #days in a week where balls get hit for homeruns ~ Poisson(35 balls/7day)
P(Z=5) = ...

Last edited: Apr 9, 2012