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NDA 2 2024 Maths, question 104

Topic: Probability

Q104

A,B,CA,B,C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B)=4P(A)3P(B)=4P(A) and 3P(C)=2P(B)3P(C)=2P(B), then what is P(A)P(A) equal to?

  1. (a) 7/297/29
  2. (b) 8/298/29
  3. (c) 9/299/29Correct answer
  4. (d) 10/2910/29

Solution.

Answer: (c) 9/299/29

  1. Let P(A)=a.
  2. Then P(B)=4a/3 and P(C)=2P(B)/3=8a/9.
  3. Mutual exclusivity and exhaustiveness give a+4a/3+8a/9=1, so 29a/9=1 and P(A)=9/29.