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. The numerator requires me to select 5 of 19 girls. The numerator will be 19C5. The denominator consists of the 5 of the 34 total students that may be selected. Answer: 19C5 / 34C5 =.0417 4.2% 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. The numerator requires me to select 4 of the 28 people with a college degree. The numerator will be 28C4. The denominator consists of 4 of the 35 people attending the dance. The denominator will be 35C4. Answer: 28C4 / 35C4 =.3910 = 39.1% 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. The numerator requires me to select 3 of the 4 people with October birthdays. The numerator will be 4C3. The denominator will be 16C3 as I may choose any 3 of the 16 people. Answer: 4C3 / 16C3 =.0071 = 0.7% 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. The numerator requires me to select 4 of the 8 students. The numerator will be 8C4. The denominator will be 15C4 as any 4 of the 15 people may be selected. Answer: 8C4 / 15C4 =.0512 = 5.1%
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. The numerator requires me to select 2 of the 4 fives. The numerator will be 4C2. The denominator will be 8C2 as I can select any 2 of the 8 bills. Answer: 4C2 / 8C2 =.2142 = 21.4% 11) 3 cards are drawn from a standard deck of cards. What is the probability they are all hearts? The numerator requires me to select 3 of the 13 hearts. The numerator will be 13C3. The denominator will be 52C3 as any 3 of the 52 cards can be selected. Answer: 13C3 / 52C3 =.0129=.013 = 1.3% 13) 2 cards are drawn from a standard deck of cards. What is the probability they are both red? The numerator requires me to select 2 of the 26 red cards. Answer: 26C2 / 52C2 =.245 = 24.5% 15) 2 cards are drawn from a standard deck of cards. What is the probability they are all queens? The numerator requires me to select 2 of the 4 queens. The numerator will be 4C2. Answer: 4C2 / 52C2 =.0045 =.5%
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. 4 of 8 boys (8C4) 8 of 19 girls (19C8) The denominator will be 34C12 as any 12 of the 34 students can be selected. Answer: (15C4 * 19C8) / 34C12 =.188 = 18.8% 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. The numerator requires me to select : 3 of 28 with college degree (28C3) 1 of 7 without college degree (7C1) The denominator will be 35C4 as any 4 of the 35 people in attendance may be selected. Answer: (28C3 * 7C1)/35C4 =.438 = 43.8% 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. 2 of 4 people with October birthdays (4C2) 1 of the 12 that don t have October birthday (12C1) The denominator will be 16C3 as any 3 of the 16 in attendance may be chosen. Answer: (4C2 * 12C1) / 16C3 =.129 = 12.9%
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. 3 of 8 students (8C3) 1 of 7 teachers (7C1) The denominator will be 15C4 as any 4 of the 15 people may be selected. Answer: (8C3 * 7C1) / 15C4 =.287 = 28.7% 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. 2 of the 4 five dollar bills (4C2) 3 of the 5 ten dollar bills (5C3) The denominator will be 11C5 as any 5 of the 11 bills may be selected. Answer: (4C2 * 5C3) / 11C5 =.1298 =.130 = 13% 27) 3 cards are drawn from a standard deck of cards. What is the probability they are two hearts and 1 spade? 2 of 13 hearts (13C2) 1 of 13 spades (13C1) The denominator will be 52C3 as any 3 of the 52 cards can be selected. Answer: (13C2 * 13C1) / (52C3) =.046 = 4.6%
29) 2 cards are drawn from a standard deck of cards. What is the probability they are 1 red and 1 black? 1 of 26 black cards (26C1) 1 of 26 red cards (26C1) Answer: (26C1 * 26C1) / 52C2 =.5098 =.510 = 51%