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Today Puzzle #601

Puzzle No. 601鈥� Thursday 31 October

It is Halloween and (Mishal) decides to make a game for the more mature trick or treaters. She/he has three 20 dollar bills, three 5 dollar ones and two 1 dollar bills in a hat. She offers the visitors the opportunity to add a further 1 dollar bill to the collection, mix them up, and take out three notes. If they are all the same value the visitor can keep them, but if not then (Mishal) does. Is this game a trick or a treat?

Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution

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The answer involves calculating the probability for each of the scenarios where the visitor will gain. The probability of the visitor drawing out a $20 bill to start with is 3/9. The probability of drawing out a $20 bill again is 2/8, and the next time is 1/7. Therefore, the probability of drawing out three $20 bills is (3/9) x (2/8) x (1/7) = 6/504. The expected value of this scenario is ($20+$20+$20) x (6/504) = $0.71. Using a similar approach for the scenarios where three consecutive $5 bills or three consecutive $1 bills are withdrawn, the expected values for these are $0.18 and $0.04 respectively. Therefore, the total expected return is $0.71+$0.18+$0.04=$0.93. Given that this is less than the $1 donated by the visitor this game can be termed a TRICK.

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