Two friends picking different lottery numbers

Question

Two friends each independently pick a lottery number from 1 to 50, all equally likely. What is the probability that they pick two different numbers?

Accepted Answer

Let the first friend pick some number; that fixes one value out of the 50. The second friend is equally likely to pick any of the 50 numbers. Exactly one of those would match the first friend, so 49 of the 50 choices are different. Therefore P(	ext{different numbers}) = \frac{49}{50} = 0.98, which is 98\%. As a check, the two possibilities must add to 1: a match happens with probability 1/50 = 0.02, and a mismatch with probability 49/50 = 0.98, and indeed 0.02 + 0.98 = 1. Takeaway. With d equally likely choices, two people differ with probability (d-1)/d and match with probability 1/d. The t…

Two friends picking different lottery numbers

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