Final answer:
The probability that at least two people in a room of 26 share a birthday is calculated using the concept of complementary probability.
Step-by-step explanation:
The calculation of the probability that at least two people in a room of 26 share a birthday is done using the concept of complementary probability.
Step 1: Calculate the probability that no two people share a birthday. To do this, we consider each person in the room and calculate the probability that they have a different birthday than all the people before them. The first person can have any birthday, so the probability is 1. The second person must have a different birthday than the first, so the probability is 365/365. The third person must have a different birthday than the first two, so the probability is 364/365. Continuing this pattern, the probability that no two people share a birthday is: (365/365) * (364/365) * ... * ((365 - (26-1))/365).
Step 2: Calculate the probability that at least two people share a birthday by subtracting the probability calculated in step 1 from 1.
The probability that at least two people in a room of 26 share a birthday is therefore: 1 - [(365/365) * (364/365) * ... * ((365 - (26-1))/365)].