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15.10.2019 •
Mathematics
There are 11 red checkers and 5 black checkers in a bag. checkers are selected one at a time, with replacement. each time, the color of the checker is recorded. find the probability of selecting a red checker exactly 6 times in 9 selections. show your work.
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Ответ:
P(6 times in 9 selection) = 0.116
Step-by-step explanation:
There are 11 red checkers and 5 black checkers in a bag so
P(red) = no. of red checkers / total no. of checkers = 11/(11+5) = 11/16
Checkers are selected one at a time, with replacement. So P(red) is the same for every selection at 11/16.
Use binomial distribution to find the probability of selecting a red checker exactly 6 times in 9 selections.
In this case, n = 9 and k = 6, P(red)=11/16 so
P(6 times in 9 selection) = nCk * P(red)^k * (1-P(red))^(n-k)
where 9C7 = 9! / [7!*(9-7)!] = 9! / 7!*2! = 9*8 / 2 =36
so P(6 times in 9 selection)
= 36 * (11/16)^6 * (5/16)^3
= 0.116
Ответ: