3,639 views
1 votes
1 votes
Out of 2000 families with 4 children each how many families would you expect to have atleast one BOY..?

2 Answers

Best answer
2 votes
2 votes

This could be solved using Binomial Distribution...

Assumption :
P ( Boy Child) = P ( Girl Child ) = 1/2

Solution :

P( atleast one Boy) = 1-p(no Boys )

                                  = C(4,0) (1/2)0 (1/2)4

                                   = 1-  1/16

                                   = 15/16

Therefore Expectation of 2000 Families

                 E(X) = 2000* 15/16

                         = 1875

1 votes
1 votes
For a family, There are 5 possibilities in having 4 childrens

 No Boy { G,G,G,G}

1 Boy    { B,G,G,G}

2 Boys  { B,B,G,G}

3 Boys  { B,B,B,G}

all boys {B,B,B,B}

For a family to have at least one boy the probability is = 4/5

So we can expect 2000* $\frac{4}{5}$ = 1600 families to have atleast one boy.

Related questions

2 votes
2 votes
5 answers
4
Pooja Palod asked Dec 16, 2015
4,668 views
A fair coin is tossed repeatedly till both head and tail appear atleast once. Average no of tosses required is ?