Question

Consider a class with 30 students. Compute the probability that at least two of them have their birthdays on the same day. (For simplicity, ignore the leap year.) (b) How many students should be in class in order to have this probability above 0.5

Answer 1

0.7063

Explanation:

Given that:

Number of students = 30

Number of days in a year = 365

P(atleast 2 people share same birthday) = 1 - p(none share same Birthday)

p(none share same Birthday) =

(365! / (365 - 30)!) * 1/365^30

(365! / 335!) * 1/365^30

365! ÷ (335! * 365^30)

= 0.2936837

P(atleast 2 people share same birthday) :

1 - 0.2936837

= 0.7063163

= 0.7063 * 100%

= 70.63%