- #1
Thecla
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538 is a website that does election data and polling analysis. On its Culture page there are some math, probability, and statistics puzzles. The following is one that stumped me:
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
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