Chapter 13.3, Problem 71AYU

To determine

To find: The probability that at least 2 people in a group of 12 people have the same birthday.

Answer to Problem 71AYU

$0.167$

Explanation of Solution

Given:

Number of people in the group is 12.

Calculation:

Probability of at least 2 people in a group of 12 having same birthday,

$=1-probabilityofnonehavingbirthdayonthesameday.$

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

$=\frac{1-365\ast 364\ast 363\ast \dots \mathrm{..354}}{{365}^{12}}$

$\approx 1-0.833=0.167$