Today Puzzle #653
Puzzle No. 653 鈥� Tuesday 14 January
There is a 50 pound note in 1 of every 100 envelopes. Your friend has made a machine which can detect the valuable envelopes with 99% accuracy and offers it to you for 30 pounds. Should you purchase it to help you choose one envelope?
Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution
Click here for the answer
The machine will select 99% of the valuable envelopes, which comprise 1% of the total. Unfortunately, the machine will also select 1% of the empty ones, which comprise 99% of the total. The expected value using the machine is therefore £50 x (99% x 1%) / (99% x 1% + 1% x 99%) = £25. This is lower than the price of the selecting machine which would therefore not be deemed to be a sensible purchase. You would be better off choosing an envelope without purchasing the machine as the expected value of that is 1% x £50 = 50p.
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