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Math Help - Binomial distribution

  1. #1
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    Post Binomial distribution

    This problem have been taken from the old paper of MASTER of COMMERCE Examination of well-known University in India.
    The probability of a man hitting a target is \frac14.How many times must he fire so that the probability of his hitting the target at least once is greater than \frac23 ?

    Answer: -
    3.818 times i-e approximately 4 times
    A man must fire 4 times so that the probability of his hitting the target at least once is greater than \frac23
    Verify the answer, if found wrong reply me.
    Answer is not available in the university paper set.So I don't know whether I solved the problem wrongly or correctly.
    Last edited by Vinod; December 25th 2011 at 03:41 AM.
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: Binomial distribution

    Quote Originally Posted by Vinod View Post
    This problem have been taken from the old paper of MASTER of COMMERCE Examination of well-known University in India.
    The probability of a man hitting a target is \frac14.How many times must he fire so that the probability of his hitting the target at least once is greater than \frac23 ?

    Answer: -
    3.818 times i-e approximately 4 times
    A man must fire 4 times so that the probability of his hitting the target at least once is greater than \frac23
    Verify the answer, if found wrong reply me.
    Answer is not available in the university paper set.So I don't know whether I solved the problem wrongly or correctly.
    By definition it must be (\frac{3}{4})^n<\frac{1}{3} \implies (\frac{4}{3})^n>3 \implies n\ \ln \frac{4}{3}>\ln 3 \implies

    \implies n> \frac{\ln 3}{\ln \frac{4}{3}} = 3.8188416793...



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    \chi \sigma
    Last edited by chisigma; December 25th 2011 at 09:20 AM.
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