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Probability Homerun Problem

  1. Apr 8, 2012 #1
    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
  2. jcsd
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