Fewpal
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A die is rolled. If the outcome is an odd number, what is the probability that it is a prime number ?

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S = {1, 2, 3, 4, 5, 6} ⇒ n(S) = 6 

Let A : Event of getting an odd number 

B : Event of getting a prime number 

A = {1, 3, 5} ⇒ n(A) = 3 

B = {2, 3, 5} ⇒ n(B) = 3 

A ∩ B = {3, 5} ⇒ n(A ∩ B) = 2 

∴ P(A) = \(\frac{n(A)}{n(S)} =\frac{3}{6} =\frac{1}{2}\)

P(B) = \(\frac{n(B)}{n(S)} =\frac{3}{6} =\frac{1}{2}\)

P(A ∩ B) =\(\frac{n(A\,\cap\,B)}{n(S)}=\frac{2}{6}=\frac{1}{3}\)

∴ P(B/A) = \(\frac {P(A\,\cap\,B)}{P(A)}=\frac{\frac{1}{3}}{\frac{1}{2}}= \frac{2}{3}\) .

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