A student takes examination in four subjects A, B, C, D. His chance of passing in A is 4/5,in B is 3/4in C is 5/6 and in D is 2/3.To qualify he must pass in A and at least two other subjects. What is the probability that he qualifies?

Answer 1

p(not pass B, C, D) = 1/4 * 1/6 * 1/3 = 1/72

p(not pass B, C) = 1/4 * 1/6 = 1/24 = 3/72

p(not pass B, D) = 1/4 * 1/3 = 1/12 = 6/72

p(not pass C, D) = 1/6 * 1/3 = 1/18 = 4/72

p(pass at least two) = 1 - 14/72 = 58/72

p(qualify) = 4/5 * 58/72