Forty people are selected at random. What is the probability that none of the people in this group have the same birthday?
as below
To find the probability that none of the people in a group of forty have the same birthday, we need to consider the total number of possible outcomes and the favorable outcomes.
Total number of outcomes:
Since there are 365 days in a year, each person can have any of these 365 possible birthdays. Therefore, the total number of outcomes is 365 raised to the power of 40 (365^40).
Favorable outcomes:
To have no same birthdays in a group of forty people, the first person can have any of the 365 birthdays. The second person then has 364 remaining possible birthdays, the third person has 363 remaining possible birthdays, and so on.
Therefore, the favorable outcomes can be calculated by multiplying the number of remaining possible birthdays for each person:
365 * 364 * 363 * ... * (365 - 39)
Finally, we can calculate the probability by dividing the favorable outcomes by the total number of outcomes:
Probability = Favorable outcomes / Total outcomes
To calculate the probability, substitute the values into the formula and calculate:
Probability = (365 * 364 * 363 * ... * (365 - 39)) / (365^40)