a student takes his examination in 4 subjects-A,B,C,D.To qualify he must pass in A and at least 2 other subjects. His chances of Passing in A,B,C,D are 4/5, 3/4, 5/6, 2/3 respectively. Find the chances of his qualifying.

Given P(A)=45, P(B)=34, P(C)=56, P(D)=23According to the condition the student will qualify when he pass in Sub A and at least 2 subjectSo, Prob that he will qualify=He pass in A and (Pass in BC or CD or BD or BCD)=P(A)[P(B)P(C)+P(C)P(D)+P(B)P(D)+ P(B)P(C)P(D)]=4534×56+56×23+34×23+34×56×23=4558+59+12+512=4545+40+36+3072=4515172=15190

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