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Suppose you are in a room with 26 people. If you ignore leap years, what is the probability that at least two of you share a birthday?

A. 0%
B. 50%
C. 95%
D. 100%

User Preetha
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1 Answer

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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)].

User JasonPlutext
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