There have been 31 no-hitters in major league baseball since the year 2000. Over

Question

There have been 31 no-hitters in major league baseball since the year 2000. Over this span,

there have been 31,590 baseball games scheduled.

a. Assuming the 2000-2012 period was representative, model the number of no-hitters as a binomial random

variable. What is an appropriate value of p, the probability of success?

b. Again assuming that no-hitters are a binomial random variable, what is the probability of there being

at least one no-hitter in the 2013 season? (hint: as there are 30 MLB teams, there are 162 *15 = 2430 games

played in one season)

c. What is the probability there are exactly 3 no-hitters in MLB next year?

d. Suppose you plan on attending two MLB games/year for the next 50 years. What is the probability

you never witness a no-hitter?

Explanation / Answer

a)    p=31/31590=.000981

b) Pr(X=0)=(2430C0)(p)^0(1-p)^2430=.0920

so prob. of at least 1 no-hitter is 1-.0920=.908

c) Pr(X=3)=(2430C3)p^3(1-p)^2427=.2083

d) 2 games/year for 50 years =100 GAMES

Pr(X=0)=(100C0)p^0(1-p)^100=.9065

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