If three people are randomly selected, find the probability that they will all have birthdays on the same day of the year.
Assuming a uniform population,
the 1st person has a birthday.
The 2nd has the same birthday with probability 1/365
same for the 3rd.
So, ...
To find the probability that three people will all have birthdays on the same day of the year, we need to consider the total number of possible outcomes and the number of successful outcomes.
Let's assume that they are not born on a leap day, so we have 365 possible days for a birthday.
The total number of possible outcomes is given by the number of ways we can choose a birthday for each person. Since each person can be born on any of the 365 days, the total number of possible outcomes is 365 * 365 * 365 = 48,627,125.
Now, let's consider the number of successful outcomes, which is the number of ways all three people can have birthdays on the same day. Since there are 365 days to choose from, there is only one successful outcome.
Therefore, the probability that three people will all have birthdays on the same day of the year is 1/48,627,125.