Three people are chosen at random and each is equally likely to have been born on any of the 7 days of the week, independently of the others. What is the probability that at least two of them were born on the same day of the week?

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Accepted Answer

19/49. Count the opposite event instead. All three born on different days happens in 7 × 6 × 5 = 210 of the 7³ = 343 equally likely triples, a probability of 210/343 = 30/49. Hence P(at least two share a day) = 1 − 30/49 = 19/49. Answering 30/49 forgets to take the complement.

Three people are chosen at random and each is equally likely to have been born on any of the 7 days of the week, independently of the others. What is the probability that at least two of them were born on the same day of the week?

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