By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2025 Maths, question 115

Topic: Probability

Q115

If P(A)=1/3P(A) = 1/3, P(B)=1/2P(B) = 1/2 and P(A∩B)=1/4P(A \cap B) = 1/4, then what is the value of P(B∣Ac)P\left( B \mid A^{c} \right)?

  1. (a) 1/8
  2. (b) 3/8Correct answer
  3. (c) 5/8
  4. (d) 7/8

Solution.

Answer: (b) 3/8

  1. The part of BB outside AA has probability P(B∩Ac)=P(B)−P(A∩B)=1/2−1/4=1/4P\left( B \cap A^{c} \right) = P(B) - P(A \cap B) = 1/2 - 1/4 = 1/4.
  2. Also P(Ac)=2/3P\left( A^{c} \right) = 2/3.
  3. Therefore P(B∣Ac)=(1/4)/(2/3)=3/8P\left( B \mid A^{c} \right) = (1/4)/(2/3) = 3/8.