Question

Savita and Hamida are friends. What is the probability that both will have (1) different birthdays ? (2) the same birthday ? (ignoring a leap year).

Answer 1

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

If Savita's bday is different from Hamida's bday, the number of favourable outcomes for her bday is 365 - 1 = 364

P(E) = (Number of outcomes favourable to E)(Total number of outcomes) = 364/365

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

P(E) + P (not E)​ = 1

Probability of Savita and Hamida sharing the same bday will be:

P (not E)​ = 1 - P(E) =( 1 - 364) /365 = 1/365