Question

a if two people are selected at random, the probability that they do not have the same birthday (day and month) is 364/365. explain why this is so. (ignore leap years and assume 365 days in a year.) the first person can have any birthday, so they can have a birthday on one of the 365 days. in order for the second person to not have the same birthday they must have one of the remaining birthdays. (type whole numbers)

Explanation:

Step1: Analyze first - person's birthday

The first person can have a birthday on any of the 365 days. So the number of choices for the first - person's birthday is 365.

Step2: Analyze second - person's birthday

For the second person to not have the same birthday as the first, given that the first person has already taken one day, the second person has 364 remaining choices out of 365 days.
The probability that two people do not have the same birthday is calculated by multiplying the probability of the first - person having any birthday (which is 1 or $\frac{365}{365}$) and the probability of the second - person having a different birthday from the first (which is $\frac{364}{365}$).
The probability that the first person has a birthday on any day is $\frac{365}{365}$ because they can choose any of the 365 days. The probability that the second person has a different birthday from the first is $\frac{364}{365}$ since there are 364 non - matching days left out of 365.

Answer:

The first blank is 365, the second blank is 364.