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August 14th, 2018, 09:43 AM   #1
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Probability Interview Question

Toss a coin until the nth Head turns up. Let Y = number of required tosses, calculate P(Y is even), set p=P(H), q=P(T).

Last edited by skipjack; August 14th, 2018 at 11:05 AM.
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August 14th, 2018, 01:53 PM   #2
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$P(Y=n)=q^{n-1}p$. Therefore $P(Y\ is\ even)=p\sum_{k=1}^{\infty}q^{2k-1}=\frac{pq}{1-q^2}=\frac{q}{1+q}$
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Last edited by mathman; August 15th, 2018 at 04:22 PM. Reason: add material
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