Determine 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, by answering the following questions.
(a) Compute the probability that 15 people have different birthdays.
(b) The complement of "15 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 15 share the same birthday.
(a) The probability that 15 people have different birthdays is (Round to three decimal places as needed.)

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 \(\boxed{1 - 0.747 = 0.253}\).