Question

Suppose we pick three people at random. For each of the following questions, ignore the special case where someone might be born on February 29th, and assume that births are evenly distributed throughout the year (a) What is the probability that the first two people share a birthday? (b) What is the probability that at least two people share a birthday?(c) What is the probability that all three people share a birthday? (d) What if there were 15 people, what is the probability that at least one pair share a birthday? (e) What if there were 23 people, what is the probability that at least one pair share a birthday?

Answer 1

a) The probability that the first two people share a birthday is 0.97 or 97%.

b) The probability that at least two people share a birthday is 0.99 or 99%.

c) The probability that all three people share a birthday is 0.0015 or 0.15%.

d) The probability that at least one pair of 15 people share a birthday is 0.58 or 58%.

e) The probability that at least one pair of 23 people share a birthday is 0.87 or 87%.