6 1. Consider a family of three children. Find the following probabilities. a. P (two girls and a boy) b. P (at least one girl) c. P (children of both sexes) d. P (at least two girls) 2. A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilities for the following events. a. At least three freshmen. b. All four of the same class. c. Not all four from the same class. d. Exactly three of the same class. 3. At a college, 60% of the students pass Accounting, 70% pass English, and 30% pass both of these courses. If a student is selected at random, find the following conditional probabilities. a. The student passes Accounting given that said student passed English. b. The student passes English given that said student passed Accounting. 4. John's probability of passing statistics is 40%, and Linda's probability of passing the same course is 70%. If the two events are independent, find the following probabilities. a. P(both of them will pass statistics) b. P(at least one of them will pass statistics) 5. A $1 lottery ticket offers a grand prize of $10,000; 10 runner-up prizes each paying $1000; 100 thirdplace prizes each paying $100; and 1,000 fourth-place prizes each paying $10. Find the expected value of entering this contest if 1 million tickets are sold. 6. Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on the next test to have an average of exactly 80 for the four tests