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Math Help - Probability problem

  1. #1
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    Probability problem

    Hey.

    I was wondering if someone could help me with this...

    A fair coin is tossed repeatedly, with successive independent tosses, until two consecutive heads OR two consecutive tails are observed. X is the number of tosses required to achieve this.

    Explain why the probability mass function of X is given by:

    P(X=n) = (1/2)^(n-1) where n=2,3,4,....


    Thank you to all x
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  2. #2
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    Quote Originally Posted by onemoretime29 View Post
    Hey.

    I was wondering if someone could help me with this...

    A fair coin is tossed repeatedly, with successive independent tosses, until two consecutive heads OR two consecutive tails are observed. X is the number of tosses required to achieve this.

    Explain why the probability mass function of X is given by:

    P(X=n) = (1/2)^(n-1) where n=2,3,4,....


    Thank you to all x
    You should try and see a pattern for the general case of n tosses by calculating the probability for n = 2, 3, 4, .....

    n = 2: Require HH or TT. Pr(n = 2) = (1/2)^2 + (1/2)^2 = 1/2.

    n = 3: ....

    n = 4: ....

    .
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    .
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