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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- Jan 2nd 2013, 12:40 PMbroccoli7The 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 - Feb 6th 2013, 07:51 AMMINOANMANRe: 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 - Feb 6th 2013, 07:16 PMzzephodRe: The Magician's Coin Tossing Experiment
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 $\displaystyle P(trick)=0.75$

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

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

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