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Math Help - The Magician's Coin Tossing Experiment

  1. #1
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    The Magician's Coin Tossing Experiment

    A magician flips a coin and claims to be able to make it always fall heads. He flips a coin and it falls heads. Do you believe in the magician's magical powers?

    Spoiler/Answer here Probability Puzzles: The Magician's Coin Tossing Experiment
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  2. #2
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    Re: The Magician's Coin Tossing Experiment

    If this were true then the whole probability theory would be rabish!!!!!!
    None can predict the outcome of a random experiment with 100% probability .....unless he(she) is doing some tricks or he uses biased tools...to foolish you.

    " Probability...something that avery one must consider ....and none to ignore....Blaise Pascal..French Mathematician & Philosopher"
    Minoas
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    Re: The Magician's Coin Tossing Experiment

    Quote Originally Posted by MINOANMAN View Post
    If this were true then the whole probability theory would be rabish!!!!!!
    We are talking about a magician, there is a real chance that when she tosses the coin it is not a random event. This calls for Bayes' theorem. Suppose prior probability that the Magician is performing a trick P(trick)=0.75

    \begin{aligned}P(trick|result)&=\frac{P(result|tri  ck)P(trick)}{P(result|trick)P(trick)+P(result|\neg  trick)P(\negtrick)}\\ \\ &=\frac{0.95\times0.75}{0.95\times0.75+0.5\times0.  25}\approx 0.8507\end{aligned}

    (note I am assuming that if it is a trick then there is a 95\% chance the result is what he says it will be)

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