# Two coins are tossed. Find the conditional probability of getting two heads given that at least one coin shows a head .

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Two coins are tossed. Find the conditional probability of getting two heads given that at least one coin shows a head .

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B: At least one coin showing a head.

S = {HH, HT, TH, HH}

Then, A = {HH}, B = {HT, TH, HH} ⇒ A ∩ B = {HH}

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