Question

Three fair coins are tossed find the probability that they are all tails, if one of the coin shows a tail

Answer 1

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Answer 2

Answer:

P(A/B) = 8/49

Step-by-step explanation:

Given:- Three coins are tossed together.

To Find:- Probability that the outcome is all tails if one of them shows a tail.

Solution:-

When 3 coins are tossed together, the possible outcomes are HHH, TTT, TTH, HTT, THT, THH, HTH, HHT.

Let A be the event that all coins show tails, the outcome will be

A = { TTT }

P( A ) = 1/8

Let's B be the event that one coin shows a tail, then the outcome will be

B = { HTH, THH, HHT, TTH, HTT, THT, TTT }

P ( B ) = 7/8

A ∩ B = { TTT }

P( A ∩ B) = 1/7

P(A/B) = P( A ∩ B)/ P(B)       [conditional probability]

          = ( 1/7 )/(7/8)

          = ( 1/7 ) × ( 8/7 )

          = 8/49

Therefore, probability that all are tails if one of the coin shows a tail = 8/49

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