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just a fast one:

Three coins 10p,20p and 50p. The values of those that land heads up are added to work out the total amount ξ. What is the expected total amount ξ given that two coins have landed heads up?

After calculating the integral I found that that the final result is 160/3... textbook says its 53/3 but I believe its wrong due to some calculation errors.

Thanks in advance

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You are correct. The book's answer is wrong.

Observe that if the top coin were 30p instead of 50p, then the average winnings would obviously be 20p. The book's answer is less than this, and therefore cannot be correct.

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Consider this

Case 1) 10, 20p heads...total can be 80 or 30

Case 2) 20p 50p heads...total can be 70 or 80

Case 3) 50p 10p heads...total can be 60 or 80

expectation = (110/2 + 150/2 + 140/2)x 1/3 (since all cases are equally probable)

so overall it is 200/3

just to add....i purposely solved it in a different way.... it's easy to see without any integration it's 160/3...from above cases...if we exclude the third toss. Problem with the question is that it's not 100% clear....i would rather say ambiguous. I guess most people will disagree!

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