# Brain Teasers are Back!

I calculate there are 25 outcomes from two spins, of which only five yield a score of 5 or more, equating to a 20% chance.
So, on 200 games, their total income is £50 (200 x £0.25).
They would expect to pay out on 20%, or 40, of those games.
Therefore, they would expect their total outlay to be £40 (40 x £1).
Their expected profit is £10 from 200 games (ie £50 less £40).
However, I’m also sure they expect their Grandfather to bail them out if the spinner doesn’t behave.

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A very clear explanation. I always like a good explanation, probably more than seeing the answer.

Your observation prompts a harder spin-off question:

What is the probability of Don being out of pocket (assuming he agrees to this!) and what are his expected losses?

Well done Steve

As Ravvie said, a very clear explanation. And the correct answer, of course !

For the benefit of others who might be browsing, I have drawn up a grid to show the possible scores with two spins ie the 25 outcomes that Steve referred to. Five of these are coloured red to highlight those with a score of 5 or more.

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Hmm, I’m struggling to work out a correct approach here. I can see that the maximum loss is £150, if every game results in a £1 payout (income £50 less payout £200).
The chances of this are presumably 0.2 to the power 200.
I seem to remember a binomial expansion, including Pascal’s Triangle, that would compute the odds every other individual occurrence (eg 199 lose - 1 win, 198 lose - 2 win etc etc).
However, I’ve no idea how you condense these calculations into something manageable.

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Yes it is a binomial expansion and Pascal’s Triangle is a good tool to use, so you are on the right lines. It was the approach I used.

I did resort to using a spreadsheet to do the calculations though, given we need the 200th row. There is a shortcut that avoids having to create the whole triangle.