Homework

Homework # 1 – 10: Two cards are selected at random from a deck of 52 cards WITHOUT replacement. Find the requested probabilities, (write your answer as a reduced fraction.) 1) Both cards are red P(1st red and 2nd red) = P(1st red)*P(2nd red) 26 52 25 25 ∗ 51 = 102 Answer: 25/102 3) The first card is a 7 and the second card is a 4 P(1st seven and 2nd four) = P(1st seven)*P(2nd four) 4 4 52 4 ∗ 51 = 663 Answer: 4/663 5) Both cards are fives P(1st five and 2nd five) = P(1st five)*P(2nd five) 4 52 3 1 ∗ 51 = 221 Answer: 1/221 7) The first card is red and the second card is black P(1st red and 2nd black) = P(1st red)*P(2nd black) 26 52 26 13 ∗ 51 = 51 Answer: 13/51 9) The first card is not a seven and the second card is a seven P(1st not seven and 2nd is a seven) = P(1st not seven)*P(2nd is seven) 48 52 4 16 ∗ 51 = 221 Answer: 16/221 Homework # 11 – 20: Two cards are selected at random from a deck of 52 cards WITH replacement. Find the requested probabilities (write your answer as a reduced fraction) 11) Both cards are hearts P(1st heart and 2nd heart) = P(1st heart)*P(second heart) 13 13 169 ∗ = 2704 52 52 Answer: 1/16 13) The first card is a six and the second card is black P(1st six and 2nd black) = P(1st six)*P(2nd black) 4 26 104 ∗ = 2704 52 52 Answer: 1/26 15) The first card is a face card and the second card is not a face card There are 12 face cards (4 jacks, 4 queens and 4 kings) There rest of the cards are not face cards. There are 40 cards that are not face cards. P(first is a face card and second not a face care) = P(first face card)*P(second not a face card) 4 40 160 10 ∗ = 2704 = 169 52 52 Answer: 10/169 17) Neither card is black P(1st not black and 2nd not black) = P(1st not black)*P(2nd not black) 26 52 26 1 ∗ 52 = 4 Answer: 1/4 19) The first card is a queen and the second card is a seven P(1st queen and 2nd seven) = P(1st queen)*P(second 7) 4 52 4 1 ∗ 52 = 169 Answer: 1/169 Homework # 21-24: The spinner below is spun twice, find the requested probabilities (write your answer as a reduced fraction.) 21) Both spins are yellow P(yellow first and yellow second) = P(yellow first)*P(yellow second) 1 5 1 1 ∗ 5 = 25 Answer: 1/25 23) The first spin is green and the second is not red P(green first and second not red) = P(green first)*P(second not red) 1 5 4 4 ∗ 5 = 25 Answer: 4/25 Homework # 25-28: The spinner below is spun three times, find the requested probabilities (write your answer as a reduced fraction.) 25) The spins in order are green, yellow the blue P(green first and yellow second and blue third) = P(green 1st)*P(yellow 2nd)*P(blue 3rd) 1 2 1 1 1 ∗ 4 ∗ 4 = 32 Answer: 1/32 27) Green is spun each time P(green first and green second and green third) = P(green first)*P(green second)*P(green third) 1 1 1 1 ∗ ∗ =8 2 2 2 Answer: 1/8 Homework #29 – 32: A coin is tossed then a dice is rolled, find the requested probabilities (write your answer as a reduced fraction.) 29) The coin is a head and the dice is a 4 P(head and dice 4) = P(coin head)*P(dice 4) 1 1 1 ∗ 6 = 12 2 Answer: 1/12 31) The coin is not a head and the dice is an even number P(coin not head and dice even) = P(coin not head)*P(dice even) 1 3 3 ∗ 6 = 12 2 Answer: 1/4 Homework #33-34: A sample of 30 women who recently had a home built yielded the following information about their builder: Number of women 19 6 5 Would you recommend builder to a friend Yes No Not sure Three women who provided information for the table were selected at random. Find the probability that: 33) The first would not recommend her home builder, but the second and third would recommend their home builder. P(1st not recommend and second will recommend and third will recommend) = P(1st does not recommend)*P(second does recommend)*P(third does recommend) 6 30 19 18 171 ∗ 29 ∗ 28 = 2030 Answer: 171/2030 Homework #35-38 Two marbles are drawn from a bag that contains 5 blue, 3 red and 2 purple marbles without replacement. Find the requested probabilities 35) Both are blue P(blue first and blue second) = P(blue first)*P(blue second) 5 4 20 ∗ = 90 10 9 Answer: 2/9 37) The first is purple and the second is not blue P(purple first and second not blue) = P(purple first)*P(second not blue) 2 10 4 4 ∗ 9 = 45 Answer: 4/45 Homework #39-42 Two marbles are drawn from a bag that contains 5 blue, 3 red and 2 purple marbles with replacement. Find the requested probabilities 39) Both are blue P(blue 1st and blue 2nd) = P(blue 1st)*P(blue 2nd) 5 10 5 1 ∗ 10 = 4 Answer: ¼ 41) The first is purple and the second is not blue P(purple 1st and second not blue) = P(purple 1st)*P(not blue second) 2 5 1 ∗ = 10 10 10 Answer: 1/10