Bhisham C. Gupta - Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP

23 A bag contains a nickel, quarter, and “dime”, with the dime being a fake coin and having two heads. A coin is chosen at random from the bag and tossed four times in succession. If the result is four heads, what is the probability that the fake dime has been used?

24 In a playground, there are 18 players, 11 of them boys and seven are girls. Eight of the boys and three of the girls are soccer players; the rest are basketball players. The name of each player is written on a separate slip, and then these slips are put into an urn. One slip is drawn randomly from the urn; the player whose name appears on this slip is given a prize. What is the probability that a soccer player gets the prize given that a boy gets the prize?

25 Let , and be mutually exclusive and exhaustive events in a sample space S, and let , and . Let B be another event in S such that . Find the probabilities and .

26 An industry uses three methods , and to train their workers. Of all the workers trained, 50% are trained by method , 28% by method , and the rest, 22%, by method . Further 10% of those trained by method do not perform their job well, while 5% trained by method and 15% by methods also do not perform their job well. A randomly selected worker does not perform his job well. Find the probability that the worker was trained by (a) method , (b) method , and (c) method .

27 Suppose that an insurance company finds that during the past three years, 60% of their policy holders have no accident, 25% had one accident, and the remaining 15% had two or more accidents. Further, from their past 10 year history, the insurance company concludes that those who did not have any accident have a 1% chance of having an accident in the future, while those who had one accident have a 3% chance of having an accident in the future. Those who had two or more accidents in the past three years have 10% chances having an accident in the future. Suppose that shortly after the above study, one of their policy holders has an accident. What is the probability that this policy holder did not have any accident in the past three years?

28 Suppose that in a bolt manufacturing plant, machines A, B, and C manufacture, respectively, 45%, 25%, and 30% of the bolts. It is observed that the three machines produce, respectively, 5%, 2%, and 3% defective bolts. If the bolts produced by these machines are mixed in a well‐mixed lot and then a randomly selected bolt is found to be defective, find the probability that the defective bolt is produced by (a) machine A, (b) machine B, and (c) machine C.

29 A poll was conducted among 1000 registered voters in a metropolitan area asking their position on bringing a casino in that city. The results of the poll are shown in the following table:SexPercentage ofPercentagePercentage notPercentagevoters polledfavoring casinofavoring casinohaving no opinionMale55%75%20%5%Female45%40%50%10%What is the probability that a registered voter selected at randomWas a man, given that the voter favored the casino?Was a woman, given that the voter has no opinion about the casino?Was a woman, given that the voter did not favor the bringing in of a casino?

30 Let a random variable be distributed as shown below.01234560.10.090.20.150.160.2Find the probability .Find the probability .Find the probability .Find the probability .

31 Determine which of the following distributions do not represent a probability distribution. Justify your answer.(a)0123450.10.090.20.150.160.2(b)012345−0.10.090.30.150.160.4(c)0123450.20.090.20.150.160.2

32 In Problem 31, construct a bar chart for the probability distribution that satisfies the conditions of a probability distribution.

33 The following Venn diagram describes the sample space S of a random experiment and events A, B, and C associated with the experiment. (S consists of 12 elements, denoted by )Express the events A, B, and C in terms of the elements .Suppose that the sample points in the sample space S are equally likely.Find the following probabilities:

Текст предоставлен ООО «ЛитРес».

Прочитайте эту книгу целиком, на ЛитРес.

Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.