# Compute probabilities and means given a distribution

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1. In a recent poll of married couples, about 79 percent of the men and 55 percent of the women were employed outside the home. In 39 percent of the couples, both the husband and the wife work outside the home.

Find the probability that in a randomly selected couple either the husband or his wife works outside the home.

2. A despondent math professor is traveling to Las Vegas to bet his entire life savings, $20,000 on one roll of the (two) dice. If the total is 7 or 11, he will take home $100,000; otherwise, he forfeits his savings.

What is his mathematical expectation?

3. According to the Bureau of Navel (sic) Standards, 75 percent of all people are "inners," (that is, their belly buttons poke inward) ; everyone else is an "outer." Let the random variable x be the number of outers among 7 randomly selected persons.

A. Find the mean and variance of x.

B. Find the probability that exactly 2 of the 7 persons are outers.

C. Find the probability that no more than 6 of the 7 are outers.

D. Find the probability that none of the 7 is an outer.

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1. In a recent poll of married couples, about 79 percent of the men and 55 percent of the women were employed outside the home. In 39 percent of the couples, both the husband and the wife work outside the home.

Find the probability that in a randomly selected couple either the husband or his wife works outside the home.

Solution. In a randomly selected couple, denote the event that the husband works outside the home by A and denote the event that his wife ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
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