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Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with probability $\dfrac{1}{4}.$ Both watch a cricket match. Arjun tells you that India won, Karan tells you that India lost. What probability will you assign to India's win?

  1. $\left(\dfrac{1}{2}\right)$
  2. $\left(\dfrac{2}{3}\right)$
  3. $\left(\dfrac{3}{4}\right)$
  4. $\left(\dfrac{5}{6}\right)$
  5. $\left(\dfrac{6}{7}\right)$
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6 Answers

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WRONG APPROACH

The answer should be 1/2 i.e option A

Arjun told: India won,

Karan told: India lost,

Probability of India won = Probability that Arjun told truth(=3/4) & Karan lied(= 2/3)

So probability that India won = (3/4)x(2/3) = 1/2.

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Case 1 : Arjun tells the truth that India won , then Karan  must lie about the fact India lost , in order India to win .

Therefore :   (3/4)*(2/3) = (1/2)

Case 2: Arjun is lieing about India's win then karan must also lie about India's loss because the motive is to make India win .

Therefore (1/4)*(2/3) = 1/6 .

Total probability for India wining is 1/2 + 1/6 = 2/3 .

Hence answer is B .
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