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Math Help - coin - prob distribution

  1. #1
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    coin - prob distribution

    I need help with the following question:

    A coin is biased to show heads twice as often as it shows tails. You toss this coin 3 times and win 1 dollar each time it shows tails but lose 50 cents each time it shows heads.

    a) What is the probability distribution of X: the amount of money you could win or lose in 3 tosses?

    b) On average, how much money would you win or lose each time you toss this coin 3 times?

    c) Express the maximum amount of money you could win in 3 tosses of this coin as a Z-score?

    a) X{-1.50, 0, 1.50, 3.00}, p(X) {0.2963, 0.4444, 0.2222, 0.037}
    b) mu = 0
    c) Z=2.45
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  2. #2
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    Quote Originally Posted by aptiva
    I need help with the following question:

    A coin is biased to show heads twice as often as it shows tails. You toss this coin 3 times and win 1 dollar each time it shows tails but lose 50 cents each time it shows heads.

    a) What is the probability distribution of X: the amount of money you could win or lose in 3 tosses?
    Let x represent the number of heads. Then,
    \left\{ \begin{array}{cc}x&P(x)\\0&.0037\\1&.2222\\2&.4444  \\3&.2963
    Thus,
    probability of
    losing 1.50 is .0037
    gaining nothing is .2222
    winning 1.50 is .4444
    wining 3 is .2963
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  3. #3
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    but how are those numbers/probabilities calculated?
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  4. #4
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    Quote Originally Posted by aptiva
    but how are those numbers/probabilities calculated?
    Hello,

    you deal with binomial distribution. The probability that the result X happens exactly k-times is with your problem:
    P(X=k)={3\choose k} \cdot \left({2\over3}\right)^k \cdot \left(1-{2\over3}\right)^{(3-k)}

    Plug in the values 0, 1, 2, 3 for k and you'll get the probabilities which ThePerfectHacker had already calculated.

    For instance: k = 0:
    P(X=0)={3\choose 0} \cdot \left({2\over3}\right)^0 \cdot \left(1-{2\over3}\right)^{(3-0)} = 1 \cdot 1\cdot \left({1\over3}\right)^{3}={1 \over 27} \approx .037


    Greetings

    EB
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