27. If P (A) = 0.5, P (B) = 0.3, P (AB) = 0.2, obtain the probability that (i) A occurs but not B (ii) At least one of A and B occurs (iii) Neither of A and B occurs.
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- I need the answer as soon as possibleAn IT company employs two sales engineers. Engineer 1 does the work of estimating cost for70% of jobs bid by the company. Engineer 2 does the work for 30% of jobs bid by the company.It is known that the error rate for engineer 1 is such that 0.02 is the probability of an error whenhe does the work, whereas the probability of an error in the work of engineer 2 is 0.04. Supposea bid arrives and a serious error occurs in estimating cost. Which engineer would you guess didthe work? Explain and show all work.Solve Q23
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- The probability that a student will pass in the Economics test is 2/3, and that a vill not pass in the English test is 5/9. If the probability of his passing in at ne ane of these two tests is 4/5 , find the probability that he will pass in both 20 is the tests. CS Scanned with CamScannerSuppose the probability that a male develops some form of cancer in his lifetime is 0.4573. Suppose the probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51, and that this probability is independent of the probability that a male will develop cancer in his lifetime. • C = a man develops cancer in his lifetime• F = a man has at least one false positive Part (a) Construct a tree diagram of the situation. P(C) = P(F | C) = P(F | C' ) If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not. -You cannot assume the man has cancer because there is not enough information given. -You cannot assume the man has cancer because there is a 51% chance that the test is false. -You cannot assume the man has cancer because both the probability of developing cancer in his lifetime and the probability of…Q2: Box 1 contains 1 white and 999 red balls. Box 2 contains 1 red and 999 white balls, A ball is picked from a randomly selected box. If the ball is red what is the probability that it came from box 1?
