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A and B are friends. Ignoring the leap year, find the probability that both friends will have ...

A and B are best friends. What are the chances that they share the same birthday?
Ignoring leap years, each person can be born on any of the 365 days with equal probability.

So we calculate:

(i) Probability they have different birthdays
First friend can have a birthday on any day.
Second friend must have a birthday on any of the remaining 364 days.
So probability = 364/365

(ii) Probability they have the same birthday
Only 1 day matches out of 365 days.
So probability = 1/365

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