Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places.
A)0.97736
B)0.84986
C)0.87286
D)0.48643
E)0.97286

Question

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​
A)0.97736
B)0.84986
C)0.87286
D)0.48643
E)0.97286

Quizplus · Accepted Answer

The probability that five people have different birthdays can be calculated by considering the fraction of the total number of ways their birthdays can be different to the total number of possible birthday combinations. For the first person, there are 365 choices out of 365. For the second person, to avoid the first person's birthday, there are 364 choices out of 365, and so on. Thus, the probability is (365/365) * (364/365) * (363/365) * (362/365) * (361/365) ≈ 0.97286.

Assuming There Are 365 Different Birthdays, Find the Probability That