In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females Round your answer to four decimal places.
A) 0.1094
B) 0.8906
C) 0.2344
D) 0.25
E) 0.0156

Question

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females  Round your answer to four decimal places.  
A) 0.1094
B)  0.8906
C)  0.2344
D)  0.25
E)  0.0156

Quizplus · Accepted Answer

We can use the binomial distribution to solve this problem.

Let X be the number of females in a sample of 6 participants. Then, X follows a binomial distribution with parameters n = 6 and p = 0.5 (since half of the participants are female).

We want to find P(X ≥ 2), which is the probability of drawing at least 2 females.

Using the binomial distribution formula or a calculator, we get:

P(X ≥ 2) = 1 - P(X < 2)
= 1 - P(X = 0) - P(X = 1)
= 1 - (0.5)⁶ - 6(0.5)⁵(0.5) - 15(0.5)⁴(0.5)²
= 0.890625

Therefore, the probability that an investigator will draw at least 2 females in a random sample of 6 participants is 0.8906 (rounded to four decimal places), which corresponds to choice B.

In a Large On-The-Job Training Program, Half of the Participants