Solution:
Out of the two friends, A’s birthday can be any day of the year. Now, B’s birthday can also be any day of 365 days in the year.
We assume that these 365 outcomes are equally likely.
So,
(i) If A’s birthday is different from B’s, the number of favourable outcomes for his birthday is 365 – 1 = 364
Hence, P (A’s birthday is different from B’s birthday) = 364/365
(ii) P (A and B have the same birthday) = 1 – P (both have different birthdays)
= 1 – 364/365 [As P (E’) = 1 – P(E)]
= 1/ 365