4 children are to be selected from a group of 3 boys and 3

Question

4 children are to be selected from a group of 3 boys and 3 girls. What is the probability that an equal number of boys and girls are selected? 

a. 1/10
b. 4/9
c. 1/2
d. 3/5
e. 2/3

 Please explain how you arrived at the answer.

UMB · Answer

/ 6C4=3/5  D.

baer · Answer

That is the OA. Why did you set it up that way. Can you explain the reasoning? Thanks.

UMB · Answer

There are 3C2 possible ways to choose 2 boys and same for girls. 
Togather there are 3C2*3C2 ways to choose 2 boys and 2 girls to the group , consisiting of 4 children.
From 6 children there are 6C4 ways to choose 4 children. 
therefore probabilityis :   / 6C4=3/5

salr15 · Answer

There are 4 spots and the only way to have even number of boys and girls is 2 girls and 2 boys.

Combination of boys:

3C2 = 3

B1 B2
B2 B3
B1 B3

Combination of girls:

3C2 = 3

G1 G2
G2 G3
G1 G3

So total possible ways to have 2 girls and 2 boys = 3*3 = 9

G1 G2 B1 B2
G1 G2 B2 B3
G1 G2 B1 B3 ...and so on

Total possible combinations:

6C4 = (6*5*4!)/(4!*2!) = 30/2 = 15

so the probabilty that 2 boys and 2 girls = 9/15 = 3/5.

andrehaui · Answer

I love prob!!!

we have 4 places for 2 boys and 2 girls

well, for 3 boys taking 2 , you have 6 possibilities of places, but you can exclude repetitions so we have only 3
12
21
13
31
23
32

for 2 girls iden, 3 possibilities

thats 3*3=9, but we still need number of total outcomes and that's 6C4

so we get 9/15 or 3/5




so you have the answer!!!

ywilfred · Answer

We need 2 boys selected. # of such groups = 3C2= 3. We have the same number of groups for girls.

So total = 3*3 = 9 such groups of 2 girls and 2 boys.

# of ways to pick 4 people from a group of 6 = 6C4 = 15

P = 9/15 = 3/5

Andrey2010 · Answer

Please explain me where I'm making the mistake:

3/6 - probability to select 1st B
2/5 - probability to select 2d B
3/4 - probability to select 1st G
2/3 - probability to select 2d G

3/6 * 2/5 * 3/4 * 2/3 = 1 / 10

Why is it wrong? And where is my mistake?

Thank you in advance.

UMB · Answer

Andrey2010
IMO u didn't take into account other possiblities.
one of them is order of selecting boys and girls. 
Try this B1, G1, G2,B2 now Try G1, B1, B2,G2 each time probability will be different.

4 children are to be selected from a group of 3 boys and 3

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