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Math Help - Probability check

  1. #1
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    Probability check

    I have a last task to do, can you guide me through please.

    - The probability of a sniper shot to strike in a single shot is "P".
    It's known that if the sniper fires 3 times then the probability that from the three shots the sniper will strike at least one time and miss at least one time is 0.48.
    A- Find "P".


    So I was able to get these two equation according to Bernoulli's table:
    3P*(1-P)^2 - 0.48 = 3P^2*(1-P)^1 - 0.48
    Are these correct ? according to the task ? can anyone check it and I'll solve it, and if It's not truth can anyone help me fix it ?
    Final equation was :
    -6P^2 +3P=0
    Final answer is : 0.8 / 0.2
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Mathematicsfan View Post
    I have a last task to do, can you guide me through please.

    - The probability of a sniper shot to strike in a single shot is "P".
    It's known that if the sniper fires 3 times then the probability that from the three shots the sniper will strike at least one time and miss at least one time is 0.48.
    A- Find "P".


    So I was able to get these two equation according to Bernoulli's table:
    3P*(1-P)^2 - 0.48 = 3P^2*(1-P)^1 - 0.48
    Are these correct ? according to the task ? can anyone check it and I'll solve it, and if It's not truth can anyone help me fix it ?
    Final equation was :
    -6P^2 +3P=0
    Final answer is : 0.8 / 0.2
    The probability of at "least 1 hit and at least 1 miss" is
    the sum of the probabilities of "2 hits and 1 miss" and 1 hit and 2 misses",
    which is, from the Binomial expansion of (p+q)^3

    \binom{3}{2}p^2(1-p)+\binom{3}{1}p(1-p)^2=0.48

    \Rightarrow\ 3\left(p^2-p^3\right)+3p\left(1-2p+p^2\right)=0.48

    \Rightarrow\ 3p^2-3p^3+3p-6p^2+3p^3=0.48

    \Rightarrow\ -3p^2+3p=0.48\Rightarrow\ p^2-p+0.16=0

    from which p=0.8,\;0.2
    are obtained.
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  3. #3
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    Thank you so much you have helped me way beyond my expectations !!!
    I finally understood it deeply.
    Thanks again !!!
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