Answer:
0.0177 days
Step-by-step explanation:
Solution:-
- The group has n = 50 people
- Each person is equally likely to have a birthday on each of 365 days in the year.
- The probability of success p = 1 / 365
- The probability of failure q = (1 - 1/365)
- We will denote random variable X as a given day has k number of birthdays.
- X follows binomial distribution:
X ~ Bi ( 50 , 1/365)
- The probability that there would be 3 birthdays on a day would be:
P ( X = 3 ) = 50C3 ( 1 / 365)^3 * ( 1 - 1/365)^47
P ( X = 3 ) = 0.00035
- The expected number of days for exactly three people to have same birth date:
E( X = 3 ) = P (X=3)*n = 0.00035*50 = 0.0177 days
