Qtb Probability free essay sample

Q. 1 A fair coin is tossed twice and two outcomes are noted. What is the probability that both outcomes are heads? Explain. Ans. P(H) = 1/2 Probability of 2 heads = 1/2 x 1/2 = 1/4 Q. 2 Suppose that 25% of the population in a given area is exposed to a television commercial on Ford automobiles, and 34% is exposed to Ford’s radio advertisements. Also, it is known that 10 % of the population is exposed to both means of advertising. If a person is randomly chose out of the entire population on this area, what is the probability that he or she was exposed to at least one of the two modes of advertising? Ans. Probability of advertisement by Tv be P(T) Probability of advertisement by radiao be P(R) Probability of advertisement by both will be P(T^R) ACTQ, P(T) = 0. 25 and P(R) = 0. 34 and P(T^R) = 0. 10 Therefore, Probability that he or she was exposed to at least one of the two modes of advertising = P(T) + P(R) + P(T^R) = 0. 25 + 0. 34 + 0. 10 = 0. 69 Q. 3 A Consulting firm is bidding for two jobs, one with each of two large multinational corporations. The company executive estimate the probability of obtaining the consulting job with firm A is 0. 45. The executives also feel that if the company gets the job with firm A, then there is 0. 90 probability that firm B will also give the company the consulting job. What are the company’s chances of getting both jobs? Ans. P(A) = 0. 45 Executive had already offered job from A, Probability that he will get job in B be P(B/A) P(B/A) = 0. 90 Probability of getting job = P(A) x P(B/A) = 0. 45 x 0. 90 = 0. 405 Q. 4 A bank loan officer knows that 12% of the bank’s mortgage holders lose their jobs and default on the loan in course of 5 years. She also knows that 20% of the bank’s mortgage holders lose their jobs during this period. Given that one of her mortgage holder just lost his job, what is the probability that he will now default on the loan? Ans. Probability of bank’s mortgage holders lose their jobs be P(B) = 0. 20 Probability of bank’s mortgage holders lose their jobs and default on the loan be P(A/B) = 0. 12 ACTQ, one of her mortgage holder just lost his job, what is the probability that he will now default on the loan = P(B/A) = P(B) x P(A/B) = 0. 20 x 0. 12 = 0. 024 Q. 5 The probability that a consumer will be exposed to an advertisement for a certain product by seeing a commercial on television is 0. 04. The probability that the consumer will exposed to the product by seeing it an advertisement on a billboard is 0. 06. The two events, being exposed to the commercial and being exposed to the billboard are assumed to be independent. Â ·What is the probability that the consumer will be exposed to both advertisements? Â ·What is the probability that he or she will be exposed to at least one of the advertisements? Ans. P(T) = 0. 04 , P(T) = 1 P(T) = 0. 96 P(B) = 0. 06 , P(B) = 1 P(B) = 0. 94 1) probability that the consumer will be exposed to both advertisements = P(T) x P(B) = 0. 04 x 0. 06 = 0. 024 2) probability that he or she will be exposed to at least one of the advertisements = P(T) x P(B) + P(T) x P(B) + P(T) x P(B) = 0. 04 x 0. 94 + 0. 06 x 0. 96 + 0. 96 x 0. 94 = ___________________ Q. 6 An economist believes that during periods of high economic growth, the U. S. dollar appreciates with probability 0. 70, in periods of moderate economic growth the dollar appreciates with pro bability 0. 40, and during periods of low economic growth, the dollar appreciates with probability 0. 20. During any period of time, the probability of high economic growth is 0. 30, the probability of moderate economic growth is 0. 0, and the probability of low economic growth is 0. 20. Suppose the dollar has been appreciating during the present period. What is the probability we are experiencing a period of high economic growth? Q. 7 A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0. 95. When an emergency situation does not exist, the alarm system sounds with probability 0. 02. A real emergency situation is a rare event, with probability 0. 004. Given that the alarm has just sounded, what is the probability that a real emergency situation exists? Q. 8 On average, a ship arrives at a certain dock every second day. What is the probability that two or more ships will arrive on a randomly selected day? Q. 9 An insurance company is considering the addition of major medical coverage for a relatively rare ailment. The probability that a randomly selected individual will have the ailment is 0. 001 and 3,000 individuals are included in the group that is insured. Â ·What is the expected number of people who will have the ailment in the group? Â ·What is the probability that no one in this group of 3,000 people will have this ailment? Q. 0 Harley Davidson, director of quality control for the Kyoto motor company, is conducting his monthly spot check of automatic transmissions. In this procedure, 10 transmissions are removed from the pool of components and are checked for manufacturing defects. Historically, only 2 percent of the transmissions have such flaws. (Assume that flaws occur independently in different transmissions. ) Â ·What is the probability that Harley’s sample contains more than two transmissions with manufacturing flaws? (Don’t use the tables). Â ·What is the probability that none of the selected transmissions has any manufacturing flaws? Q. 11 A recent study of how Americans spend their leisure time surveyed workers employed more than 5 years. They determined the probability an employee has 2 weeks of vacation time to be 0. 45, 1 week of vacation time to be 0. 10 and 3 or more weeks to be 0. 20. Suppose 20 workers are selected at random, Answer the following questions: Â ·What is the probability that 8 have 2 weeks of vacation time? Â ·What is the probability that only one worker has 1 week of vacation time? Â ·What is the probability that at most 2 of the workers have 3 or more weeks of vacation time? Q. 2 Each 500 ft roll of sheet includes two flaws, on average. A flaw is a scratch or mark that would affect the use of that segment of sheet steel in the finished product. What is the probability that a particular 100 ft segment will include no flaws? Q. 13 What is the probability of obtaining a score greater than 700 on a GMAT test that has a mean of 494 and a standard deviation of 100? Assume GMAT scores are norm ally distributed. Q. 14 For the same GMAT examination (that has a mean of 494 and a standard deviation of 100), what is the probability of randomly drawing a score that is 550 or less?