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NDA 2017 Maths · Mathematics · Probability · hard

A and B are events with P(A)=0.6, P(Bmid A)=0.5 and P(Bmid A^c=0.2. Then P(B) equals

Single correct option

A and B are events with P(A)=0.6, P(B∣A)=0.5P(A)=0.6,\ P(B\mid A)=0.5 and P(B∣Ac)=0.2P(B\mid A^c)=0.2. Then P(B)P(B) equals
  1. A. 0.30.3
  2. B. 0.380.38
  3. C. 0.50.5
  4. D. 0.70.7
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Answer: (B) 0.380.38

By total probability, P(B)=P(A)P(B∣A)+P(Ac)P(B∣Ac)=0.6(0.5)+0.4(0.2)=0.30+0.08=0.38P(B)=P(A)P(B\mid A)+P(A^c)P(B\mid A^c)=0.6(0.5)+0.4(0.2)=0.30+0.08=0.38. The value 0.30.3 is P(A∩B)P(A\cap B) only, and the others result from averaging the two conditional values without weights.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake