Section 4.9. Solving Probability Problems by Using Combinations

Section 4.9: Solving Probability Problems by Using Combinations Answers: 1) 19C5 / 34C5 = .0417 4.2% 3) 28C4 / 35C4 = .391 = 39.1% 5) 4C3 / 16C3 = .007 = 0.7% 7) 8C4 / 15C4 = .051 = 5.1% 9) 4C2 / 8C2 = .214 = 21.4% 11) 13C3 / 52C3 =.013 = 1.3% 13) 26C2 / 52C2 = .245 = 24.5% 15) 4C2 / 52C2 = .0045 = .5% 17) (15C4 * 19C8) / 34C12 = .188 = 18.8% 19) (28C3 * 7C1)/35C4 = .438 = 43.8% 21) (4C2 * 12C1) / 16C3 = .129 = 12.9% 23) (8C3 * 7C1) / 15C4 = .287 = 28.7% 25) (4C2 * 5C3) / 11C5 = .1298 = 13% 27) (13C2 * 13C1) / (52C3) = .046 = 4.6% 29) (26C1 * 26C1) / 52C2 = .5098 = 51% Homework #1-16 (Write your answer as a percent rounded to 1 decimal place.) 1) A class consists of 19 girls and 15 boys. If 5 of the students are to be selected at random, determine the probability they are all girls. 2) A club has 8 boys and 5 girls. 3 members are selected at random, determine the probability they are all boys. 3) Of 35 people attending a dance 28 have a college degree. If 4 people at the dance are selected at random, find the probability each has a college degree. 4) Of 50 people attending a concert 30 have seen the group before. If 8 people at the concert are selected at random, find the probability each has seen the group before. 5) A class of 16 people contains 4 people whose birthday is in October. If 3 people from the class are selected at random, find the probability that none of those selected has an October birthday. 6) A class of 25 people contains 5 Gemini’s. If 4 people from the class are selected at random, find the probability that none of those selected are Gemini’s. 7) A committee of 4 is to be randomly selected from a group of 7 teachers and 8 students. Find the probability the committee will consist of 4 students. 8) A committee of 4 is to be randomly selected from a group of 7 teachers and 8 students. Find the probability the committee will consist of 4 teachers 9) Anthony’s wallet contains 8 bills of the following denominations, four $5 bills, two $10 bills, one $20 bill and one $50 bill. If he selects two bills at random, determine the probability that he selects 2 $5 bills. 10) Anthony’s wallet contains 8 bills of the following denominations, four $5 bills, two $10 bills, one $20 bill and one $50 bill. If he selects two bills at random, determine the probability that he selects 2 tens. 11) 3 cards are drawn from a standard deck of cards. What is the probability they are all hearts? 12) 4 cards are drawn from a standard deck of cards. What is the probability they are all clubs? 13) 2 cards are drawn from a standard deck of cards. What is the probability they are both red? 14) 2 cards are drawn from a standard deck of cards. What is the probability they are both black? 15) 2 cards are drawn from a standard deck of cards. What is the probability they are all queens? 16) 2 cards are drawn from a standard deck of cards. What is the probability they are all jacks? Homework #17-32 (Write your answer as a percent rounded to 1 decimal place.) 17) A class consists of 19 girls and 15 boys. If 12 of the students are to be selected at random, determine the probability that 4 boys and 8 girls are selected. 18) A club has 8 boys and 5 girls. 3 members are selected at random, determine the probability that 2 boys and 1 girl is selected. 19) Of 35 people attending a dance 28 have a college degree. If 4 people at the dance are selected at random, find the probability 3 have a college degree and 1 does not. 20) Of 50 people attending a concert 30 have seen the group before. If 8 people at the concert are selected at random, find the probability that 6 have seen the group before and 2 have not. 21) A class of 16 people contains 4 people whose birthday is in October. If 3 people from the class are selected at random, find the probability that 2 have a birthday in October and 1 doesn’t. 22) A class of 25 people contains 5 Gemini’s. If 4 people from the class are selected at random, find the probability that 1 Gemini and 3 people that are not Gemini’s are selected. 23) A committee of 4 is to be randomly selected from a group of 7 teachers and 8 students. Find the probability the committee will consist of 3 students and 1 teacher. 24) A committee of 6 is to be randomly selected from a group of 7 teachers and 8 students. Find the probability the committee will consist of 4 teachers and 2 students. 25) Anthony’s wallet contains 11 bills of the following denominations, four $5 bills, five $10 bills, one $20 bill and one $50 bill. If he selects five bills at random, determine the probability that he selects 2 $5 bills and 3 tens. 26) Anthony’s wallet contains 10 bills of the following denominations, four $5 bills, two $10 bills, three $20 bill and one $50 bill. If he selects 3 bills at random, determine the probability that he selects 2 tens and a five. 27) 3 cards are drawn from a standard deck of cards. What is the probability they are two hearts and 1 spade? 28) 4 cards are drawn from a standard deck of cards. What is the probability they are 2 clubs and 2 diamonds? 29) 2 cards are drawn from a standard deck of cards. What is the probability they are 1 red and 1 black? 30) 5 cards are drawn from a standard deck of cards. What is the probability they are 3 black and 2 red? Answers: 1) 19C5 / 34C5 = .0417 4.2% 3) 28C4 / 35C4 = .391 = 39.1% 5) 4C3 / 16C3 = .007 = 0.7% 7) 8C4 / 15C4 = .051 = 5.1% 9) 4C2 / 8C2 = .214 = 21.4% 11) 13C3 / 52C3 =.013 = 1.3% 13) 26C2 / 52C2 = .245 = 24.5% 15) 4C2 / 52C2 = .0045 = .5% 17) (15C4 * 19C8) / 34C12 = .188 = 18.8% 19) (28C3 * 7C1)/35C4 = .438 = 43.8% 21) (4C2 * 12C1) / 16C3 = .129 = 12.9% 23) (8C3 * 7C1) / 15C4 = .287 = 28.7% 25) (4C2 * 5C3) / 11C5 = .1298 = 13% 27) (13C2 * 13C1) / (52C3) = .046 = 4.6% 29) (26C1 * 26C1) / 52C2 = .5098 = 51%