8. Thinking, Inquiry, Problem Solving There are 25 students in a Data
Management class. Determine the probability that at least two of them
share the same birthday. (Assume that every year has 365 days.)
this question requires conditional probability
i.e. probability of A = 1 - probability of B
so we have 25 people.
therefore the first persons birthday is 1/365.
the probability that the next person does not have the same birthday is 364/365.
third is 363/365.
fourth is 362/365.
so when we get to the 25th person, the probability that the birthdays are different is:
364/365 * 363/365 * 362/365 * ... * 341/365.
therefore the probability that one person has the same birthday as the other in 1 - this answer.
= 1 - 0.431300296
which is approximately 57%.