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Chapter 3: Q.3.36 (page 100)
Stores , and have , and employees, respectively, and , and percent of them respectively are women. Resignations are equally likely among all employees, regardless of sex. One woman employee resigns. What is the probability that she works in store ?
The probability that she works in storeis.
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A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that there is an 80 percent chance that she will get the job if she receives a strong recommendation, a 40 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate, and weak are .7, .2, and .1, respectively.
(a) How certain is she that she will receive the new job offer?
(b) Given that she does receive the offer, how likely should she feel that she received a strong recommendation? a moderate recommendation? a weak recommendation?
(c) Given that she does not receive the job offer, how likely should she feel that she received a strong recommendation? a moderate recommendation? a weak recommendation?
(a) An urn containswhite and black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that with probability , they are all white. Hint: Imagine that the experiment continues until all the balls are removed, and consider the last ball withdrawn.
(b) A pond containsdistinct species of fish, which we will call the Red, Blue, and Greenfish. There are Red, Blue, and Greenfish. Suppose that the fish are removed from the pond in random order. (That is, each selection is equally likely to be any of the remaining fish.) What is the probability that the Redfish are the first species to become extinct in the pond?
Hint: Write , and compute the probabilities on the right by first conditioning on the last species to be removed.
A recent college graduate is planning to take the first three actuarial examinations in the coming summer. She will take the first actuarial exam in June. If she passes that exam, then she will take the second exam in July, and if she also passes that one, then she will take the third exam in September. If she fails an exam, then she is not allowed to take any others. The probability that she passes the first exam is. If she passes the first exam, then the conditional probability that she passes the second one is , and if she passes both the first and the second exams, then the conditional probability that she passes the third exam is .7.
(a) What is the probability that she passes all three exams?
(b) Given that she did not pass all three exams, what is the conditional probability that she failed the second exam?
A total of percent of the women and percent of the men who took a certain“quit smoking” class remained nonsmokers for at least one year after completing the class. These people then attended a success party at the end of the year. If percent of the original class was male,
(a) what percentage of those attending the party were women?
(b) what percentage of the original class attended the party?
The following method was proposed to estimate the number of people over the age of 50 who reside in a town of known population 100,000: “As you walk along the streets, keep a running count of the percentage of people you encounter who are over 50. Do this for a few days; then multiply the percentage you obtain by 100,000 to obtain the estimate.” Comment on this method. Hint: Let p denote the proportion of people in the town who are over 50. Furthermore, let α1 denote the proportion of time that a person under the age of 50 spends in the streets, and let α2 be the corresponding value for those over 50. What quantity does the method suggest estimate? When is the estimate approximately equal to p?
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