101. We are given three boxes as follows: Box I has 10 light bulbs of which 4 are defective. Box Il has 6 light bulbs of which 1 is defective. Box Ill has 8 light bulbs of which 3 are defective. We select a box at random and then draw a bulb at random. Wha is the probability p that the bulb is defective? C. 13/40 a. 113/360 d. 17/40 b. 119/360 102. Three fair coins are tossed. Find the probability that they are a heads if one of the coins is a head. c. 1/7 a. 1/4 d. 3/4 b. 1/8 103. Two digits are selected at random from the digits 1 through 9. If the sum is even, find the probability that both numbers are odd. a. 3/8 c. 1/2 b. 5/8 d. 3/4 104. Four people, called North, South, East and West, are each dealt 13 cards from an ordinary deck of 52 cards. If North and South together have nine hearts, find the probability that East and West each has two hearts. a. 123/432 c. 234/575 b. 635/896 d. 142/411 105.A class has 12 boys and 4 girls. If three students are selected at random from the class, what is the probability that they are all boys? a. 3/4 c. 5/7 b. 11/15 d. 11/28 106.An urn contains 7 red marbles and 3 white marbles. Three marbles are drawn from the urn one after the other. Find the probability that the first two are red and the third is white. a. 7/10 c. 7/40 b. 2/3 d. 3/8 107.Let A and B be events with P(A) = 1/2, P(B) = 1/3, and P(An B) = 1/4. Find P(A'|B'). a. 5/6 b. 5/7 c. 5/8 d. 5/9108. In a certain college, 4%% of the men and 1% of the women are taller than 6 feet. Furthermore, 60% of the students are women. Now if a student is selected at random and is taller than 6 feet, what is the probability that the student is a woman? c. 5/11 a. 3/11 d. 9/11 b. 7/11 109.Box A contains nine cards numbered 1 through 9, and box B contains five cards numbered 1through 5. A box is chosen at random and a card drawn. If the number is even, find the probability that the card came from box A. a. 2/9 C. 4/9 b. 19/45 d. 10/19 110.An urn contains 3 red marbles and 7 white marbles. A marble is drawn from the urn and a marble of the other color is then put into the urn. A second marble is drawn from the urn. If both marbles were of the same color, what is the probability that they were both white? a. 17/50 c. 21/50 b. 12/25 d. 7/8 111. Box A contains 8 items of which 3 are defective, and box B contains 5 items of which 2 are defective. An item is drawn at random from each box. If one item is defective and the other is not, what is the probability that the defective item came from box A? a. 9/19 c. 9/40 b. 19/40 d. 3/20 112. The probabilities that three men hit a target are respectively 1/6, 1/4 and 1/3. Each shoots once at the target. If only one hit the a. 1/12 target, what is the probability that it was the first man? b. 6/31 c. 5/36 d. 31/72 113.A certain type of missile hits its target with probability 0.30. At least how many missiles should be fired so that there is at least an 80% a. 3 probability of hitting a target? b. 5 C. 4 d. 6114. In a certain town, 40% of the people have brown hair, 25% have brown eyes, and 15% have both brown hair and brown eyes, person is selected at random from the town. If he has brown eyes what is the probability that he does not have brown hair? c. 2/5 a. 3/8 d. 3/5 b. 5/8 115. Let S = (a, b, c, d, e, f) with P(a) = 1/16, P(b) = 1/16, P(c) = 1/8 P(d) = 3/16, P(e) = 1/4 and P(f)= 5/16. Let A = (a, c, e], B = (c, d e, f) and C = {b, c, f]. Find P(BIC). c. 5/8 a. 7/8 d. 1/8 b. 3/8 116. Let S = {a, b, c, d, e, f) with P(a) = 1/16, P(b) = 1/16, P(c) = 1/8, P(d) = 3/16, P(e) = 1/4 and P(f)= 5/16. Let A = {a, c, e], B = (c, d, e, f) and C = {b, c, f). Find P(CIA'). a. 2/3 c. 2/7 b. 2/5 d. 2/9 117.An urn contains 5 red marbles and 3 white marbles. A marble is selected at random from the urn, discarded, and two marbles of the other color are put into the urn. A second marble is then selected from the urn. Find the probability that both marbles are of the same color. a. 13/36 c. 15/52 b. 15/42 d. 5/9 118. We are given two urns as follows: Urn A contains 5 red marbles, 3 white marbles and 8 blue marbles. Urn B contains 3 red marbles and 5 white marbles. A fair die is tossed; if 3 or 6 appears, a marble is chosen from B, otherwise a marble is chosen from A. Find the probability that a white marble is chosen. a. 1/3 c. 2/3 b. 5/6 d. 1/6 119.A box contains 5 radio tubes of which 2 are defective. The tubes are tested one after the other until the 2 defective tubes are discovered. What is the probability that the process stopped on the third test? a. 0.20 c. 0.40 b. 0.30 d. 0.50120.A box contains 5 radio tubes of which 2 are defective. The tubes are tested one after the other until the 2 defective tubes are discovered. If the process, stopped on the third test, what is the probability that the first tube is not defective? c. 5/8 a. 2/3 b. 1/6 d. 3/10 121.A sample of 3 items is selected at random from a box containing 12 items of which 3 are defective. Find the expected number of defective items. c. 2 a. 1 b. 3 d. 4 122.Concentric circles of radius 1 and 3 inches are drawn on a circular target of radius 5 inches. A man receives 10,5 or 3 points according if he hits the target, inside the smaller circle, inside the middle annular region or inside the outer annular region respectively. Suppose the man hits the target with probability 1/2 and then is just as likely to hit one point of the target, as the other. Find the expected number of points he scores each time he fires. a. 1.96 C. 4.45 b. 2.64 d. 3.33 123.JP Sarmiento arranged all the kids in the birthday party in a circle. There were 100 kids in the party. JP Sarmiento instructed the kids to immediately poke the kid to either its left or right, with equal probability. If JP Sarmiento will give prizes to those unpoked kids, how many prizes must he expect to give away after the very short but fun game? a. 10 c. 25 b. 33 d. 50 124. Team A has probability 2/3 of winning whenever it plays. If A plays 4 games, find the probability that A wins more than half of the games. a. 8/27 b. 80/81 c. 1/3 d. 16/27 boys than girls. 125.A family has 6 children. Find the probability that there are fewer a. 5/16 b. 31/64 c. 11/32 d. 51/128126. Let X be a random variable with the standard normal distribution Find P(1X) = 0.5). c. 0.3830 a. 0.1915 d. 0.2584 b. 0.1292 127. Suppose the temperature T during June is normally distributed with mean 68 degrees and standard deviation 6 degrees. Find the probability that the temperature is between 70 degrees and 80 degrees. a. 0.25 C. 0.35 b. 0.45 d. 0.55 128.Suppose the heights H of 800 students are normally distributed with mean 66 inches and standard deviation 5 inches. Find the number of students with heights greater than or equal to 6 feet. a. 296 c. 92 b. 200 d. 352 129.A fair die is tossed 180 times. Find the probability that the face 6 will appear between 29 and 32 times inclusive. a. 0.23 c. 0.16 b. 0.29 d. 0.45 130.Among 10,000 random digits, find the probability that the digit 3 appears at most 950 times. a. 0.02 c. 0.03 b. 0.04 d. 0.05 131.Suppose 2% of the items made by a factory are defective. Find the probability that there are 3 defective items in a sample of 100 items. a. 0.18 c. 0.25 b. 0.65 d. 0.01 132. The painted light bulbs produced by a company are 50% red, 30* green and 20% blue. In a sample of 5 bulbs, find the probability that 2 are red, 1 is green and 2 are blue. a. 0.09 c. 0.11 b. 0.13 d. 0.15133.A box contains 6 red, 9 blue and 5 green balls. If you will draw a ball 7 times with replacement. Find the probability of getting 1 blue, 4 green and 2 red balls. a. 0.017 c. 0.213 b. 0.623 d. 0.942 134.A cyclone enters a certain country with a mean of approximately 9 weeks (exponentially distributed). Find the probability that the next cyclone will be coming at least six weeks from the last cyclone. a. 0.87 c. 0.51 b. 0.24 d. 0.05 135.A and B are friends. They decided to meet between 1 PM to 3 PM on a given day. There is a condition that whoever will come first will not wait for the other more than 20 minutes. Find the probability that they will meet on the same day. a. 5/52 c. 11/36 b. 9/94 d. 32/103