How do you answer question 25?

Question

25. Henry plays a game in which a coin is tossed #10# times. If it comes up heads then an extra half is added to his money. If it comes up tails then his money is halved. If starting with #$5120# Henry gets exactly #5# heads out of #10# tosses then what is the maximum amount of money he can end up with?

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Answer 1 · 2017-02-28T00:01:14

#"25."# #$1215#

Here's an approach to question #25#.

Notice that winning multiplies Henry's holdings by #3/2#, while losing multiplies his holdings by #1/2#.

So it does not matter in what order he wins and loses - the result will be:

#$5120 * (3/2)^5*(1/2)^5 = $5120 * 3^5/2^10 = $5120 * 243/1024 = $1215#

Ouch!