Question

Out of 128 families with 4children each,how many expected to have least one boy and one girl
about:(probability theoretical distribution)

Answer 1

Answer:

Among 128 families, this would be 112.5

Step-by-step explanation:

In the problem statement mentioned that atleast 1 boy and atleast 1 girl, it means family can have 2 girls,2 boys or 1 girl,3boys and 1boy, 3 girls.

Let us take probability case for atleast one girl;

0 girls- 4C0=1

1 girl- 4C1=4

2 girls- 4C2=6

3 girls- 4C3=4

4 girls- 4C4=1

Total=1+4+6+4+1=16

But our requirement is only last four are valid cases,so probability is(4+4+6+1)/16=15/16

Similarly probability for having atleast one boy would be;

=15/16

Now probability for having atleast one boy AND one girl;

= 15/16 x 15/16 = 225/256

Among 128 families, this would be= 128 x 225/256= 112.5

Answer 2

Answer:

112 Families

Step-by-step explanation:

4children in a family can be in

2 * 2 * 2 * 2 = 16 ways

at least one boy and one girl  = Total cases - all boys - all girs

All boys = 1 case

All girls = 1 case

=> at least one boy and one girl  = 16 - 1 - 1 = 14

Probability of at least one boy and one girl   = 14/16

out of 128 families expected to have = 128  * 14/16  =  8 * 14

= 112

112 Families expected to have at least one boy and one girl