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NDA2019MathematicsProbabilityActual

There are 3 coins in a box. One is a two-headed coin; a fair coin another is; and third is biased coin that comes up heads 75 % of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

Options

  1. A2 9
  2. B1 3
  3. C4 9
  4. D5 9

Correct answer

C. 4 9

Step-by-step solution

aligned & P(T)= 1 3 ; P ( H T )=1 & P(F)= 1 3 , P ( H F )= 1 2 & P(B)= 1 3 , P ( H B )= 3 4 & P ( T H )= P(T) P ( H T ) P(T) P ( H T )+P(F) P ( H F )+P(B) P ( H B ) & P ( T H )= 1 3 1 3 + 1 6 + 1 4 & = 1 9 4 = 4 9 aligned

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