Question

In a two child family,one child is a boy.What is the probability that the other child is a girl?
    $\eqalign{
  & (A)\dfrac{1}{3} \cr
  & (B)\dfrac{1}{2} \cr
  & (C)\dfrac{2}{3} \cr
  & (D)\dfrac{1}{6} \cr} $

Answer 1

Hint: Here we will use the classical definition of the theory of probability. The probability of an event A is given by $P(A) = \dfrac{m}{n}$ ,where m is the no. of cases favourable to the event A and n is the total no of cases or event points.

Complete step-by-step answer:
Step1:Here the event is A=’the other child to be a girl’.
Step2: Given, the family has two children and among them one is boy.Hence the other one may be boy or girl.So,the no of cases favourable to A i,e. m=1,as only one child may be girl.
Step3:In the event space,there will be one boy and one girl.The total no of event points will be n=2.
Step4:Then by using the above definition of the classical theory of probability ,
$$\eqalign{
  & P\left( A \right) = \dfrac{m}{n} = \dfrac{1}{2} \cr
  & or,\,P\left( A \right) = \dfrac{1}{2} \cr
  & or,\,P('the\,\,other\,\,child\,\,to\,\,be\,\,a\,\,girl') = \dfrac{1}{2} \cr
  & where\,P\,means\,the\,probability. \cr} $$
Hence the probability that the other child is a girl is $$\dfrac{1}{2}$$.So,option (B) is correct.

Note: Similarly,the probability of getting head of tossing a coin is $$\dfrac{1}{2}$$.Here the events are unbiased i,e. equally probable and mutually exclusive and disjoint also for fulfilling the criteria of the classical theory of probability.For any event A ,the probability P(A) is given by $0 \leqslant P(A) \leqslant 1$.If P(A)=1,then it is called a complete event and if P(A)=0,then it is called a null event.