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Question

A JEE aspirant estimates that he will be successful with an 80% chance if he studies 10 hr/day, with 60% chance if he studies 7 hr/day, and with 40% chance if he studies 4 hr/day. Further, he believes that he will study 10 hr, 7 hr and 4 hr per day with probability 0.1, 0.2 and 0.7 respectively. Given that he is successful, the probability that he studies for 4 hr/day equals pq where p and q are relatively prime. Then the value of (qp) is

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Solution



Let S be the event that aspirant is successful.
Then, P(C | S)=P(C)P(S | C)P(A)P(S | A)+P(B)P(S | B)+P(C)P(S | C)
P(C | S)=0.7×0.40.1×0.8+0.2×0.6+0.7×0.4
P(C | S)=712=pq
p=7,q=12
Hence the value of qp is 5.

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