In a large job-training program, 60% of the participants are men and 40% are wom

Question

In a large job-training program, 60% of the participants are men and 40% are women. An evaluator randomly identified a sample of 5 participants to estimate participate satisfaction with the program. 1. What is the probability the sample of 5 participants will not include any men? 2. What is the probability the sample of 5 participants will not include exactly 2 women?
In a large job-training program, 60% of the participants are men and 40% are women. An evaluator randomly identified a sample of 5 participants to estimate participate satisfaction with the program. 1. What is the probability the sample of 5 participants will not include any men? 2. What is the probability the sample of 5 participants will not include exactly 2 women?
In a large job-training program, 60% of the participants are men and 40% are women. An evaluator randomly identified a sample of 5 participants to estimate participate satisfaction with the program. 1. What is the probability the sample of 5 participants will not include any men? 2. What is the probability the sample of 5 participants will not include exactly 2 women?

Explanation / Answer

We have Pmen = 0.60 , Pwomen = 0.40, n= 5

1. Not include any men means all 5 members will women

p ( will not include any men ) = 0.45 = 0.01

2. The event Not include exactly 2 women is compliment of include exactly 2 women.

Out of 5, 2 will be women hence remaining three will be men.

p ( include exactly 2 women ) = 0.42 * 0.63 = 0.0346

p ( not include exactly 2 women ) = 1 - p ( include exactly 2 women ) = 1 - 0.0346 = 0.9654

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