Engineering company has a t of checking compressive strength for 100 concrete cubes. The results revealed that 85 cubes passed the compressive strength test successfully and 15 cubes failed in the test. If 10 cubes are selected at random to be inspected by the company, determine the probability that the 8 cubes will pass the test and 2 cubes will fail in the test by using the Combinatorial Analysis. *0.4522 a) 0.3415 b) 0.6553 c) 0,1156 0.2919

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James Obrien · Accepted Answer

Total number of cubes=100 Number of cubes passed the test successfully=85 Number of failed in the test=15 It is given that if 10 cubes are selected at random to be inspected by the company then we have to find the probability that 8 cubes will pass the test and 2 cubes will fail in the test. Total possible cases =100C10 Favorable cases =85C8×15C2 Required probability =Favorable casesTotal possible cases ={85}C8×15C2{100}C10 4.8125×1010×1051.731×1013 =2.7801×1051000 =291.921000 =0.2919 Thus, the required probability that 8 cubes will pass the test and 2 cubes will fail in the test is 0.2919. Hence,option(e) is correct.

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