Three fair coins are tossed. Find the probability that the outcomes are all tails, if atleast one of the coins shows a tail.

Explanation

Here, S={HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Let A = event that one of the coins shows a tail.
B = event that every coin shows a tail.
then, A={HHT, HTH, THH, HTT, THT, TTH, TTT}
B={TTT}
Clearly, `AcapB={TTT}`
`therfore " " P(A)=(n(A))/(n(S))=7/8`
`P(B)=(n(B))/(n(S))=1/8`
`P(AcapB)=(n(AcapB))/(n(S))=1/8`
`therefore` " " Required probability = P(B\A)
`=(P(AcapB))/(P(A))=(1/8)/(7/8)=1/7`