Final answer:
The correct probability that two people randomly selected from a 48-student class share the same birthday, with all days being equally likely, is roughly 0.0027 or 0.27%. This answer is not listed among the provided multiple-choice options.
Step-by-step explanation:
To calculate the probability that two people selected from a class of 48 students have the same birthday, we assume that birthdays are evenly distributed and ignore leap years. We start by calculating the probability that they do not have the same birthday and then subtract that from 1 to find the complement.
The first person can have a birthday on any day of the year, so the probability is 1 for them. For the second person to not have the same birthday, they can have any of the remaining 364 days out of 365, which gives us a probability of 364/365.
The probability that two people do not have the same birthday is:
(364/365)
To find the probability that they do have the same birthday, we subtract this from 1:
1 - (364/365) = (365/365) - (364/365) = (1/365)
So, the probability is approximately 0.0027 or around 0.27%, which is not one of the offered options. The confusion here might result from a misinterpretation of what is known as the birthday paradox, but this refers to the probability that in a group, at least two people share the same birthday, which is different from the scenario being asked about where only two individuals are selected.