Qtb Probability
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
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