Three coins are tossed. If at least one of th | vedclass

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(A) When three coins are tossed,the total sample space $S$ is given by:$S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$,where $n(S) = 8$.Let $F$ be th

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$\frac{1}{7}$

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(A) When three coins are tossed,the total sample space $S$ is given by:$S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$,where $n(S) = 8$.Let $F$ be the event that at least one coin shows a tail.$F = \{HHT, HTH, THH, HTT, THT, TTH, TTT\}$,so $n(F) = 7$.Let $E$ be the event that all three coins show a tail.$E = \{TTT\}$.Since $E$ is a subset of $F$,$E \cap F = E = \{TTT\}$,so $n(E \cap F) = 1$.The conditional probability that all three coins show tail given that at least one shows tail is $P(E|F) = \frac{n(E \cap F)}{n(F)} = \frac{1}{7}$.

Three coins are tossed. If at least one of them shows tail,then the probability that all three coins show tail is:

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