Question

The probability that three friends have same birthday if they were born in the same year (1997) is -​

Answer 1

Answer:

Step-by-step explanation:

This question is easy to calculate. Let's find the probability that all three were born on January 1. From our assumption of equally likely days, we see that each has the probability of  1365 , and from our assumption of independence, we know we can multiply these probabilities together to get the probability that all three were born on Jan 1. So the answer is  (1365)3 .

Now it's easy to see that the probability that they were all born on Jan 2 is equal to the probability that they were all born on Jan 1. In fact, this same probability is shared by all 365 days of the year. Furthermore, the event "all born on Jan 1" is disjoint from the even "all born Jan 2." In fact all 365 days represent disjoint events. That means we can find the probability that they were all born on Jan 1 or Jan 2 or Jan 3 or ... or Dec 30 or Dec 31 by summing each of those (equal) probabilities. Since there are 365 terms to be summed and each has value  (1365)3 , the result must be:

p=365⋅(1365)3=13652=1133,225