Question

1.Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.] P(A | B) = .4, P(B) = .1, P(A | B') = .6. Find P(B | A).

2.Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]

P(X | Y) = 0.6, P(Y' ) = 0.7, P(X | Y' ) = 0.1. Find P(Y | X).

3.Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]

Y₁, Y₂, Y₃ form a partition of S. P(X | Y₁) = .7, P(X | Y₂) = .2, P(X | Y₃) = .1, P(Y₁) = .3, P(Y₂) = .1.

Find P(Y₁ | X).

4.In fall 2014, 38% of applicants with a Math SAT of 700 or more were admitted by a certain university, while 18% with a Math SAT of less than 700 were admitted. Further, 34% of all applicants had a Math SAT score of 700 or more. What percentage of admitted applicants had a Math SAT of 700 or more? (Round your answer to the nearest percentage point.)

5.In a certain year, 28.3% of all light vehicles were light trucks, 28.3% were SUVs, and 43.4% were cars. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table. What is the probability that the victim of a deadly side-impact accident was driving an SUV? (Round your answer to four decimal places.)

Light Truck	.210
SUV	.371
Car	1.000

6.In a survey in a certain year of married couples with earnings, 91% of all husbands were employed. Of all employed husbands, 72% of their wives were also employed. Noting that either the husband or wife in a couple with earnings had to be employed, find the probability that the husband of an employed woman was also employed. (Round your answer to four decimal places.)

7.According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were a third as likely to develop diabetes compared with men who were sedentary. Assume that one-fourth of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active? (Round your answer to four decimal places.)

Answer 1