Question

Tina and Seenu are friends. What is the probability that both will have (i) different birthdays (ii) the same birthday? (ignoring leap years)

• A. $\frac{364}{365},\frac{1}{365}$
• B. $\frac{1}{365},\frac{364}{365}$
• C. $\frac{2}{365},\frac{363}{365}$
• D. $\frac{363}{365},\frac{2}{365}$

Answer 1

The correct option is A

$\frac{364}{365},\frac{1}{365}$

(i) Let E be the event of both having different birthdays, and (not E)​ be the event of both sharing the same day.

If Tina's is different from Seenu's, then the number of favourable outcomes for her birthday is 365 - 1 = 364

P(E) = $\frac{\text{(Number of outcomes favourable to E)}}{\text{(Total number of outcomes)}}$ = $\frac{364}{365}$

(ii) We know the sum of probabilities will always be equal to be 1,

P(E) + P (not E)​ = 1

Probability of Tina and Seenu sharing the same birthday will be:

P (not E)​ = 1 - P(E) = 1 - $\frac{364}{365}$ = $\frac{1}{365}$