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AP EAMCET20226 Jul 2022Morning ShiftMathematicsProbabilityActual

Two persons P and Q are considering to apply for a job. The probability that P applies for the job is 1 / 4 , the probability that P applies for the job given that Q applies for the job is 1 / 2 , and the probability that Q applies for the job given that P applies for the job is 1 / 3 . Then the probability that P does not apply for the job given that Q does not apply for the job is

Options

  1. A4 5
  2. B5 6
  3. C7 8
  4. D11 12

Correct answer

A. 4 5

Step-by-step solution

Given P ( P )= 1 4 , P ( P Q )= 1 2 , P ( Q P )= 1 3 . P ( P Q )=? Now, P ( Q R )= 1 3 aligned & P ( P Q ) P ( P ) = 1 3 & P ( P Q )= 1 3 1 4 = 1 12 aligned So, P ( P Q ) P ( Q ) = 1 2 aligned & P(Q)=2 1 12 = 1 6 & P( Q )=1-P(Q)=1- 1 6 = 5 6 & P( P )=1-P(P)=1- 1 4 = 3 4 & P( P Q )=1-P(P Q) & =1- 1 12 = 11 12 aligned Then, P ( P Q )= P ( P )+ P ( Q )- P ( P Q ) aligned & = 3 4 + 5 6 - 11 12 & = 18+20-22 24 = 38-22 24 = 16 24 = 2 3 aligned Now, P ( P Q )= P ( P Q ) P ( Q ) = 2 3 5 6 = 4 5

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