GATE 2017 CS (CS2) – Question 36
P applies for a job with probability 1/4. P(P applies | Q applies)=1/2 and P(Q applies | P applies)=1/3. Find P(P does not apply | Q does not apply).
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Correct answer: (A) $4/5$
Explanation
The intersection probability is (1/4)(1/3)=1/12. Using the other conditional gives P(Q)= (1/12)/(1/2)=1/6. Hence P(neither)=1−1/4−1/6+1/12=2/3. Divide by P(not Q)=5/6 to get (2/3)/(5/6)=4/5, A.