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Joe DiMaggio's record 56 game hitting streak is considered hard to break(getting at least one base hit in 56 consecutive games)

The question was what is the probability of a .300 hitter breaking this record in a 20 year baseball career?

The simplifying assumptions are:

a) The hitter gets 4 at-bats in each game

b) he plays in 160 games/year in each of his 20 years of playing.

c) There are no walks or sacrifice flies in his plate appearances

d) a hitting streak can span across seasons

I got part of the puzzle right but I couldn't complete it

The parts I got right

A)The probability of getting one hit in a game

.3^1 x .7^3=.1029x4=41.16%,since there are 4 ways of getting one hit

probability of 2 hits in a a game is .0441x6=26.46% since there are 6 ways of doing this

similarly 3 hits in a game ,the probability is 7.56%

and 4 hits in a game the probability is 0.81%

The sum is the probability of getting at least one hit in a game is 75.99%

The other part I think is right is the probability of a 57 game hitting streak is : (0.7599)^57

Now the part where I am confused.

How do you figure out the probability of getting this streak in a 3200 game career(160 games per year x 20 years)?

T