Question

A surprising result that appears in many elementy discussion on probability is called the birthday problem. The question simply stated is that if we pola certain number of people, what is the probability that at least two of those people were bom on the same day of the you? To solve this problem, use the formula for computing the probability of a complement of an event. It is clear that duplication of some birthdays) = 1 - Pino duplications. Assume that there are people. Find the probability that at least of the people were bom on the same day of the year. Do not consider February 29 (in leap years) when finding the probability The probability (Type an integer or decimal rounded to three decimal places as needed.)

Answer 1

Total people (n) = 6

We have to find probability of atleast 2 of the 6 people were born on the same day.

Suppose,

P(A) ={ atleast 2 person born on the same day.}

P(A') ={ no two person born on same day}

365 days in a year.

Therefore, sample space n(s) = 365⁶.

n(A') = {365, 364,363,362,361,360} = 365p₆

P(A') = (365p₆/365^6) = 0.9595

$\therefore P(A) = 1 - P(A')$

$\therefore P(A) = 1 - 0.9595 = 0.0405$

Hence, Probability of atleast 2 of the 6 people were born on the same day = 0.0405