Section 4.7 Conditional Probability. Homework

Section 4.7: Conditional Probability Homework #1 – 8: Create a reduced sample space and find the requested probabilities. A family has three children. Assuming that boys and girls are equally likely, determine the probability that the family has… (Write your answer as a reduced fraction.) 1) Two girls given the first child is a girl 2) Two girls given the first child is a boy 3) Less than 2 girls given the first child is a girl 4) More than 2 girls given the first child is a girl. 5) Two boys given the middle child is a boy. 6) 1 boy given the middle child is a girl 7) 1 girl given the oldest child is a girl 8) Two girls given the oldest child is a girl. Homework #9 – 16: Create a reduced sample space and find the requested probabilities. A pair of dice is rolled and the sum of the dice is recorded, determine the probability that: (Write your answer as a reduced fraction.) 9) The sum is greater than 5 given the first dice is a 4. 10) The sum is greater than 9 given the second dice is a 6. 11) The sum is even given the second dice is a 4 12) The sum is odd given the first dice is a 3 13) A double is rolled given neither dice is a 4 14) A double is not rolled given the sum is greater than 10 15) The sum is less than 3 given the first dice is a 2 16) The sum is greater than 10 given the first dice is a 3 Homework #17-24: Create a reduced sample space and find the requested probabilities. One card is selected from a deck of cards find the probability that: (Write your answer as a reduced fraction.) 17) The card is heart given it is not black 18) The card is a spade given it is red 19) The card is a four given that it is black 20) The card is a queen given that it is a face card 21) The card is not a seven given it is between 3 and 8 inclusive 22) The card is not a seven given it is between 3 and 8 exclusive 23) The card is not red given it is a queen 24) The card is not black given it is a two Homework: #25 – 28 Assume that a hat contains 4 bills: a $1 bill, a $5 bill, a $10 bill and a $20 bill. Two bills are to be selected at random with replacement. Construct a sample space, and find the probability that: (Write your answer as a reduced fraction.) 25) Both bills are $1 bills if given the first selected is a $1 bill 26) Both bills have a value greater than a $5 bill given the second bill is a $10 bill. 27) The second bill is a five given the first bill is a $5. 28) The first bill is a five given the second bill is a $5. Homework #29 – 32: At a zoo, a sampling of children was asked if the zoo were to get one additional animal, would they prefer a lion or an elephant. The results of the survey follow: (Write your answer as a reduced fraction.) Boys Girls Total Lion 90 75 165 Elephant 110 85 195 Total 200 160 360 If one child who was in the survey is selected at random, find the probability that 29) The child selected the lion, given the child is a girl. 30) The child is a boy, given the child preferred the elephant. 31) The child selected is a girl, given that the child preferred the lion. 32) The child preferred the elephant given they are a girl. Homework #33-36: A quality control inspector, is checking a sample of light bulbs for defects. The following table summarizes her findings. (Write your answer as a reduced fraction.) Wattage 20 50 100 Total Good 80 100 120 300 Defective 15 5 10 30 Total 95 105 130 330 If one of these light bulbs is selected at random, find the probability that the light bulb is 33) Good given it is 100 watts 34) Defective given it is 50 watts 35) 100 watts given it is good 36) 50 watts given it is defective Homework #37 – 40: A survey of students to determine if they had a pierced ear was given. The results are summarized in the table below. (Write your answer as a reduced fraction.) If one person is selected at random find the probability that 37) Female given they are pierced 38) Male given they are not pierced 39) Not pierced given they are female 40) Not pierced given they are male Answers: 1) 2/4 = ½ 3) 1/4 5) 2/4 = ½ 7) ¼ 9) 5/6 11) 3/6 = ½ 13) 5/25 = 1/5 15) 0/6 = 0 17) 13/26 = ½ 19) 2/26 = 1/13 21) 20/24 = 5/6 23) 2/4 = ½ 25) ¼ 27) ¼ 29) 75/160 = 15/32 31) 75/165 5/11 33) 120/130 = 12/13 35) 120/300 = 2/5 37) 288/324 = 8/9 39) 32/320 = 1/10