Problem Solving

Brent@GMATPrepNow wrote:Source: Beat The GMAT Practice Questions

A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
a) 1/126
b) 1/120
c) 1/24
d) 4/25
e) 1/2

I thought I'd re-post the question here so people don't have to keep going back to see it.
Cheers,
Brent

soubhg wrote:My logic:
Required number of cases (R)= number of ways selecting W-marble or B-marble
= 10C5*2

To find total number of cases (T):
5 girls and 5 boys are arranged in 10 chairs . Number of ways = 10|/(5|*5|)= 10C2.
Now 5 W-marbles and 5 B-marbles are arrnaged in 10 chairs. No. of ways = 10|/(5|*5|) = 10C2.

Hence reqd. prob. = R/T = 2/(5C2) = 1/126.

This is how I formulated the problem.

Comments from GMAT instructors are highly solicited.

I'm not sure if I follow this solution. It would help me assess your solution if you provided a little more text for each step. For example, I'm not really sure what you are doing when you arrange the children and marbles in the chairs.

This could very well be a good approach, I just can't tell what you are doing exactly.

Also, at the end, you write: probability = R/T = 2/(5C2) = 1/126
But, 5C2 = 10, so 2/(5C2) is actually equal to 2/20 (or 1/10), not 1/126

Cheers,
Brent

Taniuca wrote:Could someone explain to me, why the prob of being a woman is not included in the calculation?
I would thought the prob should be
(prob woman)*prob of white ball
5/10*5/10+4/9*4/9+3/8*3/8+2/7+2/7+1/6*1/6

To answer the question, we need only determine the probability that the men all receive the same colored marble, since this implies that the women all receive the same colored marble as well.

Consider this example: A box contains a white chip and a black chip. You randomly select a chip and I select the remaining chip.
What is the probability that you get the white chip and I get the black chip?
Notice that the second part (Brent gets the black chip) is somewhat redundant here. If you select the white chip then my selecting the black chip is guaranteed.
So, we could reword the question to simply read "What is the probability that you get the white chip," since the second part (Brent gets the black chip) is implied.

The same goes for the original question; once the men all receive the same colored marble, the women are guaranteed to receive the same colored marble as well.

Cheers,
Brent

Rastis wrote:Can someone please work out the math? I'm not coming up with the answer when i multiply the fractions out.

The calculations you are referring to depend on which solution you are referring to.

My solution requires us to find this product: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1

Notice that we can simplify terms as we go.

1 x 4/9 x 3/8 x 2/7 x 1/6 x 1 - the 4 and 8 can be simplified to get:
1 x 1/9 x 3/2 x 2/7 x 1/6 x 1

From here, we can simplify the 3 and 9 in 1 x 1/9 x 3/2 x 2/7 x 1/6 x 1 to get:
1 x 1/3 x 1/2 x 2/7 x 1/6 x 1

Finally, we can simplify the 2 and 2 in 1 x 1/3 x 1/2 x 2/7 x 1/6 x 1 to get:
1 x 1/3 x 1/1 x 1/7 x 1/6 x 1, which equals 1/126

Cheers,
Brent