Three coworkers, three different birth months?

Question

Three coworkers meet for the first time. Assume each person's birth month is equally likely to be any of the 12 months, independently of the others.

What is the probability that all three were born in different months?

Accepted Answer

Bring them in one at a time and require each new month to avoid the earlier ones. - The first person's month is unconstrained: probability 	frac{12}{12} = 1. - The second must differ from the first: probability 	frac{11}{12}. - The third must differ from both: probability 	frac{10}{12}. Multiply: P(	ext{all different}) = 1 	imes \frac{11}{12}	imes\frac{10}{12} = \frac{110}{144} = \frac{55}{72} \approx 0.764. So there's about a 24% chance at least two share a birth month, higher than most people guess. Takeaway. "All distinct" among independent uniform draws is a falling product, \frac{1…

Three coworkers, three different birth months?

Your answer

More Probability questions