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  • A die is thrown 6 times. If 'getting an odd number' is a success, what is the probability of (ii) at least 5 successes?

Q. 1   A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of 

             (ii) at least 5 successes?

Answers (1)

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X be a number of success of getting an odd number.

P(probability\, of\, getting\, odd\, number)=\frac{3}{6}=\frac{1}{2}

\therefore \, \, \, \, q=1-P=1-\frac{1}{2}=\frac{1}{2}

X has a binomial distribution.

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

       P(X=x)=^6C_6_-_x.(\frac{1}{2})^{6-x} . (\frac{1}{2})^{x}

       P(X=x)=^6C_6_-_x.(\frac{1}{2})^{6}

      

    P(At \, \, least \, \, 5\, \, \, success) =P(x\geq 5)

                                  =P(X=5)+P(X=6)

                                 = ^6C_5 .(\frac{1}{2})^6+^6C_6 .(\frac{1}{2})^6

                                = 6 .(\frac{1}{64})+ (\frac{1}{64})

                               = \frac{7}{64}

Posted by

seema garhwal

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