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  • A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

Q. 2  A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes

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A pair of dice is thrown 4 times.X be getting a doublet.

Probability of getting doublet in a throw of pair of dice :

                 P=\frac{6}{36}=\frac{1}{6}

               q=1-P=1-\frac{1}{6}=\frac{5}{6}

X has a binomial distribution,n=4

 \therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

         P(X=x)=^4C_x.(\frac{5}{6})^{4-x} . (\frac{1}{6})^{x}

       P(X=x)=^4C_x.\frac{5^{4-x}}{6^4}

      Put  x = 2

            P(X=2)=^4C_2.   \frac{5^{4-2}}{6^4}

           P(X=2)=6\times \frac{25}{1296}

           P(X=2)= \frac{25}{216}        

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seema garhwal

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