Question

Use a spreadsheet or calculator to determine the minimum number of people in a room to give a probability of at least 1/2 that 2 or more people share the same birthday.

a) 20

b) 23

c) 30

d) 365

Answer 1

The minimum number of people in a room to give a probability of at least 1/2 that 2 or more people share the same birthday is 23.

Step-by-step explanation:

To determine the minimum number of people in a room to give a probability of at least 1/2 that 2 or more people share the same birthday, we can use the concept of the Birthday Paradox. The probability can be calculated using the formula:

P = 1 - (365!/[(365-n)! * 365^n])

where n is the number of people in the room.

1. For option a) 20, the probability is approximately 0.4114.
2. For option b) 23, the probability is approximately 0.5073.
3. For option c) 30, the probability is approximately 0.7063.
4. For option d) 365, the probability is 1 (since all possible birthdays are covered).

Therefore, the minimum number of people in a room to give a probability of at least 1/2 is 23, so the correct answer is option b) 23.