According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the probability that at least eight were
Married?
A)0.167
B)1.002
C)0.013
D)0.161

Question

Quizplus · Accepted Answer

The probability of at least eight women being married is the complement of the probability of seven or fewer women being married. The probability of seven or fewer women being married is the sum of the probabilities of zero, one, two, three, four, five, six, or seven women being married. Using the binomial distribution, we can calculate these probabilities as follows:P(X = 0) = (0.6)^10 = 0.000006P(X = 1) = 10 * (0.6)^9 * (0.4)^1 = 0.000096P(X = 2) = 45 * (0.6)^8 * (0.4)^2 = 0.000648P(X = 3) = 120 * (0.6)^7 * (0.4)^3 = 0.00288P(X = 4) = 210 * (0.6)^6 * (0.4)^4 = 0.009072P(X = 5) = 252 * (0.6)^5 * (0.4)^5 = 0.02304P(X = 6) = 210 * (0.6)^4 * (0.4)^6 = 0.0432P(X = 7) = 120 * (0.6)^3 * (0.4)^7 = 0.0648Therefore, the probability of at least eight women being married is:1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)) = 1 - 0.167 = 0.833Therefore, the correct answer is A.

According to Government Data, the Probability That a Woman Between