Step 5 Step 4Refer to the values we have previously determined, N = 15, M = 9, n = 6, and k = 6. The remaining values needed for the formula are N - M and n - k.Find N - M.NM = 15 - 9= 6Find n - k.n-k= 6 - 6= 0Step 5Refer to these values from the previous step.N = 15, M = 9, n = 6, k = 6, N - M = 6, n k = 0Substitute these values into the hypergeometric probability formula, or use technology. Round your final answer to four decimal places.N - MP(x = k)P(x = 6)==6MCKCn-kCnC6⁹C06C6²15NTherefore, the probability of selecting six brown M&Ms from a candy dish containing nine brown and six red M&Ms is Tutorial ExerciseA candy dish contains nine brown and six red M&Ms. A child selects six M&Ms without checking the colors.What is the probability that all the M&Ms are brown?Step 1First, we need to make sure the hypergeometric distribution is appropriate for this sample. We check that 0.05, where n = 6 is the number of M&Ms being selected, and Nanswer to two decimal places.)N615nN== 0.4nThe ratio isN0.40ChP(x = k)is greater than 0.05, so we can=Step 2Recall that a hypergeometric distribution population contains M successes and N M failures. Consider drawing a brown M&M to be a success and a red M&M to be a failure.Given a total of nine brown and six red M&Ms in the dish, the total number of M&Ms was found in the previous step to be N = 15, and the total successes (or brown M&Ms) is M = 9Step 3Refer to the formula below for the probability of exactly k successes in a random sample of size n.СкМСп-кcnCNcan use the hypergeometric probability distribution for this calculation.N - M-= 15 is the total number of M&Ms in the bowl. (Round your6With nine brown M&Ms in a bowl of fifteen M&Ms, we know M = 9 and N = 15. The remaining variables are the sample size n and the number of successes k. We know that six M&Ms are drawn, and we are calculating the probability of havingexactly six brown M&Ms in that sample. Thus, in the sample of size n = 66the number of successes, or brown M&Ms, is k = 6I9

The probability shows how likely an event occurs.

Refer to these values from the previous step. N = 15, M = 9, n = 6, k = 6, N-M= 6, n-k = 0 Substitute these values into the hypergeometric probability formula, or use technology. Round your final answer to four decimal places. N-M P(x = k) = P(x = 6) = Ck Cn-k MC N Cn C6 Co 15 Therefore, the probability of selecting six brown M&Ms from a candy dish containing nine brown and six red M&Ms is