How do you answer question 25?

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How do you answer question 25?

25. Henry plays a game in which a coin is tossed $10$ $10$ 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 $$ 5120$ $$5120$ Henry gets exactly $5$ $5$ heads out of $10$ $10$ 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

$25.$ $"25."$ $$ 1215$ $$1215$

Explanation:

Here's an approach to question $25$ $25$ .

Notice that winning multiplies Henry's holdings by $\frac{3}{2}$ $3/2$ , while losing multiplies his holdings by $\frac{1}{2}$ $1/2$ .

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

$$ 5120 \cdot {(\frac{3}{2})}^{5} \cdot {(\frac{1}{2})}^{5} = $ 5120 \cdot \frac{3^{5}}{2^{10}} = $ 5120 \cdot \frac{243}{1024} = $ 1215$ $$5120 * (3/2)^5*(1/2)^5 = $5120 * 3^5/2^10 = $5120 * 243/1024 = $1215$

Ouch!

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How do you answer question 25?

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