Step 1 :We are asked to find the probability that at least 2 people in a room of 15 people share the same birthday, ignoring leap years and assuming each birthday is equally likely.
Step 2 :To solve this problem, we first need to compute the probability that all 15 people have different birthdays.
Step 3 :For the first person, there are 365 days they could be born on, so the probability is \(\frac{365}{365} = 1\).
Step 4 :For the second person, there are 364 days left, so the probability is \(\frac{364}{365}\).
Step 5 :For the third person, there are 363 days left, so the probability is \(\frac{363}{365}\), and so on until the 15th person, where there are 351 days left, so the probability is \(\frac{351}{365}\).
Step 6 :The total probability is then the product of these individual probabilities, which is approximately 0.747.
Step 7 :Thus, the probability that 15 people have different birthdays is \(\boxed{0.747}\).
Step 8 :The complement of '15 people have different birthdays' is 'at least 2 share a birthday'. So, to find the probability that at least 2 people out of 15 share the same birthday, we subtract the probability that all 15 people have different birthdays from 1.
Step 9 :Final Answer: The probability that at least 2 people out of 15 share the same birthday is \(\boxed{1 - 0.747 = 0.253}\).