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

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