(Q27) Sarada and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (ignoring a leap year).

Solution :

Out of the two friends, one girl, say, Sarada's birthday can be any day of the year.Now, Hamida's birthday can also be any day of 365 days in the year. We assume that these 365 outcomes are equally likely.

(i) If Hamida's birthday is different from Sarada's, the number of favourable outcomes for her birthday is - =

  So, P (Hamida's birthday is different from Sarada's birthday) =

(ii) P(Sarada and Hamida have the same birthday) = 1 - P (both have different birthdays)

  = 1 -
[ Using P(Ē) = 1 - P(E)] =