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Problem Of The Week # 307 - Apr 24, 2018

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Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,198
Here is this week's POTW:

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John tosses $6$ fair coins, and Mary tosses $5$ fair coins. What is the probability that John gets more "heads" than Mary?

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Remember to read the POTW submission guidelines to find out how to submit your answers!
 
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Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,198
Congratulations to castor28 for his correct solution to this week's POTW, which was Problem 99 in the MAA Challenges. His solution follows:

Let us call a "good" outcome either a head by John or a tail by Mary. Good / bad outcomes constitute a Bernoulli process with $11$ trials and probability $\dfrac12$.

John will win (get more heads than Mary) if there are $6$ good outcomes out of $11$. Because of the symmetry of the binomial distribution, this will happen with probability $\dfrac12$.
 
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