Final answer:
The correct answer is B. The number of people needed for the probability of at least one person having the same birthday as you to be greater than one half is 23.
Step-by-step explanation:
In order to calculate the number of people needed for the probability of at least one person having the same birthday as you to be greater than one half, we can use the concept of complement probability. We can calculate the probability of no one having the same birthday as you and subtract it from 1.
The probability of the first person not having the same birthday as you is 364/365. The probability of the second person not having the same birthday is 363/365, and so on. So, the probability of no one having the same birthday as you in a group of n people is (364/365)*(363/365)*...*(365-n+1)/365.
We want this probability to be less than half, so we can set up the inequality (364/365)*(363/365)*...*(365-n+1)/365 < 1/2. Solving this inequality, we find that n > 23. Therefore, the answer is B) 23.