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August 14th, 2018, 10:43 AM  #1 
Newbie Joined: Aug 2018 From: United States Posts: 3 Thanks: 0  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 12:05 PM. 
August 14th, 2018, 02:53 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,642 Thanks: 626 
$P(Y=n)=q^{n1}p$. Therefore $P(Y\ is\ even)=p\sum_{k=1}^{\infty}q^{2k1}=\frac{pq}{1q^2}=\frac{q}{1+q}$
Last edited by mathman; August 15th, 2018 at 05:22 PM. Reason: add material 

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