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There are two coins, one unbiased with probability 1/2 of getting heads and the other one is biased with probability 3/4 of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected is
  • a)
    2/3
  • b)
    3/5
  • c)
    1/2
  • d)
    2/5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
There are two coins, one unbiased with probability 1/2of getting heads...
H → Event of head showing up  
B → Event of biased coin chosen
UB → Event of unbiased coin chosen
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There are two coins, one unbiased with probability 1/2of getting heads...
Problem:

There are two coins, one unbiased with probability 1/2 of getting heads and the other one is biased with probability 3/4 of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected is

Solution:

Let U be the event of selecting an unbiased coin and B be the event of selecting a biased coin. Let H be the event of getting a head. We need to find the probability of selecting an unbiased coin given that we got a head.

Step 1: Find the probability of getting a head.

P(H) = P(H | U) * P(U) + P(H | B) * P(B)

P(H) = 1/2 * 1/2 + 3/4 * 1/2

P(H) = 5/8

Step 2: Find the probability of selecting an unbiased coin given that we got a head.

P(U | H) = P(H | U) * P(U) / P(H)

P(U | H) = 1/2 * 1/2 / 5/8

P(U | H) = 2/5

Therefore, the probability that the unbiased coin was selected given that we got a head is 2/5. The correct option is (D).
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There are two coins, one unbiased with probability 1/2of getting heads and the other one is biased with probability 3/4 of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected isa)2/3b)3/5c)1/2d)2/5Correct answer is option 'D'. Can you explain this answer?
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