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Math Help - Probability Question regarding tossing of a coin

  1. #1
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    Probability Question regarding tossing of a coin

    Question :

    How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?
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    Quote Originally Posted by zorro View Post
    Question :

    How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?
    Find the number of tosses such that Pr(no heads) = 0.125.

    Note that if X is the random variable 'number of heads' then X ~ Binomial(n = ?, p = 1/2) and Pr(X = 0) = 0.125. Substitute into the usual formula and solve for n.
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    How did u get that

    Quote Originally Posted by mr fantastic View Post
    Find the number of tosses such that Pr(no heads) = 0.125.

    Note that if X is the random variable 'number of heads' then X ~ Binomial(n = ?, p = 1/2) and Pr(X = 0) = 0.125. Substitute into the usual formula and solve for n.


    How did u get Pr(no heads) = 0.125.

    Please explain
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    Quote Originally Posted by zorro View Post
    How did u get Pr(no heads) = 0.125.

    Please explain
    Quote Originally Posted by zorro
    [snip]probability of getting atleast one head is 0.875
    Pr(no heads) = 1 - Pr(at least one head).

    You need to review the basic rules relating to complementary events.
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    I am still having problem

    Quote Originally Posted by mr fantastic View Post
    Pr(no heads) = 1 - Pr(at least one head).

    You need to review the basic rules relating to complementary events.
    Mr fantastic i still dont know how should i find 'n'

    using Binomial

    p(x,n,\theta) = \binom{n}{x} \theta^x (1- \theta)^{n-x}

    p(0,n,0.5) = \binom{n}{0} (0.125)^0 (0.875)^{n}............Is this what u meant by substituting in the usual Binomial formula
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    Quote Originally Posted by zorro View Post
    Question : How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?
    Can you solve 1-(0.5)^n\ge 0.875 for n?
    That is the essence of this question.
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    One more problem

    Quote Originally Posted by Plato View Post
    Can you solve 1-(0.5)^n\ge 0.875 for n?
    That is the essence of this question.



    1 - (0.5)^n \ = \ 0.875

    0.5^n \ = \ 1 - 0.875

    0.5^n \ = \ 0.125

    0.5 \  = \ (0.125)^{1/n}..........I am stuck here

    I know its silly but i have forgotten how to do this ........can u please help
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    Quote Originally Posted by zorro and edited (replaced equality with inequality signs) by Mr F View Post
    1 - (0.5)^n \geq \ 0.875

    0.5^n \leq 1 - 0.875

    0.5^n \leq 0.125

    [snip]
    Find (I suggest by trial and error) the minimum integer value of n that satisfies this inequality.
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  9. #9
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    Thank u Mr fantastic

    Quote Originally Posted by mr fantastic View Post
    Find (I suggest by trial and error) the minimum integer value of n that satisfies this inequality.

    n = 3

    Thank you mr fantastic for helping me
    cheers
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