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.

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