Chapter 13.3, Problem 72AYU

Birthday Problem What is the probability that at least 2 people in a group of 35 people have the same birthday? Assume that there are 365 days in a year.

To determine

To find: What is the probability that at least 2 people in a group of 12 people have the same birthday?

Answer to Problem 72AYU

$0.814$

Explanation of Solution

Given:

Number of people in the group is 35.

Calculation:

Probability of at least 2 people in a group of 35 having same birthday,

$=1-probabilityofnonehavingbirthdayonthesameday.$

$=1-\frac{n\left(differentbirthday\right)}{n\left(S\right)}$

$=\frac{1-365\ast 364\ast 363\ast \dots \mathrm{..330}}{{365}^{35}}$

$\approx 1-0.186=0.814$