We assume that the probability of a family having n children is apn for n = 1, 2,…

(where a is a positive real number such that apn

We also assume that boys and girls are equally likely to be born.
(i) Show that the probability a family with n children to have exactly k girls is

(ii) Establish that the probability a family has k girls, for k ≥ 1, is 2apk∕(2 − p)k+1;
(iii) Suppose it is known that a certain family has at least one girl. What is the probability that this family has two or more girls?

Transcribed Image Text:

n (K) 2"