Question

What is the probability that a group of five friends all have different birthdays? Show all of your work for full credit.

Answer 1

Answer: 0.98630136986

Step-by-step explanation:

There are 365 possible birthdays. The key to assigning the probability is to think in terms of complements: “Two (or more) people share a birthday” is the complement of “All people in the group have different birthdays.” Each probability is 1 minus the other. What is the probability that any two people have different birthdays? The first person could have any birthday (p = 365÷365 = 1), and the second person could then have any of the other 364 birthdays (p = 364÷365). Multiply those two and you have about 0.9973 as the probability that any two people have different birthdays, or 1−0.9973 = 0.0027 as the probability that they have the same birthday. If you have a group of five, it would mean your equation would have to be (p=360÷365)