Neeraj and Dheeraj are friends. Find the probability of their birthdays when
(i) birthdays are different.
(ii) birthdays are same.

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Solution

Case (i)
Probability of Neeraj's birthday is, $P_{1} = \frac{1}{365}$
This reduces the sample space for Dheeraj's birthday by 1 as birthday is on a different day
Probability of Dheeraj's birthday is, $P_{2} = \frac{1}{364}$
Hence, probability of Neeraj's and Dheeraj's birthday are $\frac{1}{365}$ and $\frac{1}{364}$

Case (ii)
Probability of Neeraj's birthday is, $P_{1} = \frac{1}{365}$
This reduces the sample space for Dheeraj's birthday to 1 as birthday is on the same day which is now known
Probability of Dheeraj's birthday is, $P_{2} = \frac{1}{1}$
Hence, probability of Neeraj's and Dheeraj's birthday are $\frac{1}{365}$ and $1$

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