1,001 views
1 votes
1 votes
I was doing this question using conditional probability formula.... i.e P(2/1)=? Probability of 2nd child to be boy given that 1st child is a boy. By formula, P(2/1)=P(2,1)/P(1) which is equal to P(2).P(1)/P(1)...since second child to be boy doesn't depend on first child and vice versa. So independent..Please provide the detailed solution and correct me if I am wrong.

P(2,1)= probability of 2nd and 1st child both to be boys.

1 Answer

3 votes
3 votes
Two children :-

Possibilities :-

B B

G G

B G

G B

P(One Boy Child) = $\frac{3}{4}$

P(Both Boy / One Boy Child) = (P(Both Boy) and P(One Boy child) )/ P(One Boy Child) =

$\frac{(\frac{1}{4}) } {\frac{3}{4}} = \frac{1}{4}*\frac{4}{3} = \frac{1}{3}$

 

This can also be seen more intuitively like :-

It has been said that one of the children is a boy.

So our sample space reduces to only 3 possibilities:-

B B

B G

G B

Out of the three , only one has both as boy.

Thus required P = $\frac{1}{3}$
edited by

Related questions

0 votes
0 votes
2 answers
2
radha gogia asked Feb 2, 2016
3,350 views
I did it from conditional probability , first case when we pick one spade first and then pick king nextso it is equal to ,probability of picking up a spade*probability o...
2 votes
2 votes
1 answer
3
gatecse asked Sep 15, 2014
1,659 views
A man visits a couple who have 2 children. one of the children, a boy, comes into the room. find the probability p that the other is also a boy.(a)1/3(b)2/3(c)1/2(d)3/4
5 votes
5 votes
2 answers
4
radha gogia asked Dec 21, 2015
722 views
52 cards are equally given to 4 players a,b,c,d. a and b have together total 8 spades among them. Find probability that c has 3 spades out of remaining 5.In this ques , s...