Chapter 7.E, Problem 56E

Joe Record. One of longest-standing records

in sports is the 56-game hitting streak (in baseball) Joe Dimaggio.

Assume that a player on a long •hot streak- is bat-

ting. 400. which is abotut the best that anyone ever hits over a

period of 50 or more games (A batting average of .400 means the

batter gets a hit 40% of the time. Typically, only a handful of

players each year hit that well for a long 56 games.)

a. What is the probability that a player batting -400 will get at

least one hit in four at-bats?

b. Use the result in part (a) to calculate the probability Of

a hitter getting a hit in one stretch of 56 consecutive

assuming four at-bats per game.

c. suppose that, instead Of batting .400. a player has a more

ordinary average 0f .300. In that case, what is the probability

of the player getting a hit in one stretch of 56 consecutive

Vines, assuming four at-bats per game?

d. Considering the results in parts (b) and (c) and the fact

that baseball has been played for about 100 years. are you

surprised that someone a record Of hitting in 50 consecu-

tive games? Explain clearly.