Question

According to government data, the probability that a woman between 25 and 29 was never married is 40%. In a random survey of 10 women, what is the probability that two or fewer were never married? Options:

A. 1.002
B. 0.013
C. 0.161
D. 0.167

Answer 1

The probability that two or fewer out of 10 women were never married is approximately 0.161.

Step-by-step explanation:

In this question, we are given that the probability that a woman between 25 and 29 was never married is 40%. We are asked to find the probability that two or fewer out of 10 women were never married.

To solve this, we can use the binomial probability formula. The probability of getting at most 2 women who were never married can be calculated using the formula:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = k) = C(n, k) * p^k * (1 - p)^(n-k)

where n is the number of trials (10), k is the number of successes (0, 1, or 2), p is the probability of success (0.40), and C(n, k) is the combination of n and k (n! / (k! * (n-k)!)). Hence, plugging in the values and calculating the probabilities for each value of k, we find that the probability is approximately 0.161.