# Two coins are tossed. What is the conditional probability of two tails given that at least one coin shows a tail.

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Two coins are tossed. What is the conditional probability of two tails given that at least one coin shows a tail.

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Let A : Getting two tails,

B : Getting at least one tail

Sample space S = {HH, HT, TH, TT}

A = {TT},

B = {HT, TH, TT}.

A ∩ B = {TT}

P(A) = $\frac{1}{4}$ , P(B) =$\frac{3}{4}$$(A\,\cap\,B)=\frac{1}{4}$

∴ Required probability = $P(A/B)=\frac{P(A\,\cap\,B)}{P(B)}=\frac{1/4}{3/4}=\frac{1}{3}$.