Hussain15 wrote:

From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the

probability that equal numbers of boys and girls will be selected?

A.1/10

B.4/9

C.1/2

D.3/5

E.2/3

So we are asked - what is probability of selecting 2 boys and 2 girls right:

We were not told about the actual selection, hence Before finding the probability, we should find what the different ways in which we can select 4 children.

So select 1 boy, then 1 boy, then 1 girl and then 1 girl or you can also select 1 B, 1 G, 1 B and 1 G.

Basically selecting 4 from BBGG. ie. 4 * 3 * 2 *1 / (2! * 2!) ways of making the selection. = 6.

Probability of selecting 1st boy = 3/6

Probability of selecting 2nd boy = 2/5 (as we have already selected one boy above)

Probability of selecting 1st Girl = 3/4

Probability of selecting 2nd Girl = 2/3

Multiply all of above with different ways of selecting the children =

P (selecting 2 boys and 2 girls) = 3/6 * 2/5 * 3/4 * 2/3 * 6 = 3/5

Answer : D