Ages Galore
Two different aged men meet each other in a restaraunt. They dine together, and the waiter asks them what their ages are. They both lie, and randomly say an age from 36 to 85. Assuming that both of the men's ages are actually in this range (inclusive), what is the probability that they each say the other man's ages? Express as a decimal (0.6=60%). Round to nearest ten millionth.
The answer is 0.0004165.
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1 solution
When the men lied, they chose a number from 49 numbers (36 to 85 except their true age), so the probability that they each say the other man's ages is 4 9 1 × 4 9 1 = 0 . 0 0 0 4 1 6 5 .