A box contains 5 green, 4 yellow and 3 white marbles.

Question

A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same color?

A) 3/44

B) 3/55

C) 52/55

D) 41/44

E) 1/22

Bunuel · Answer

Let's find the probability that three drawn marble are of the same color and subtract that from 1.

P(three marbles are NOT of the same color) = 1 - P(three marbles are of the same color) =

= 1- (P(all three are green) + P(all three are yellow) + P(all three are white)) =

= 1- (\frac{5C3}{12C3} + \frac{4C3}{12C3} + \frac{3C3}{12C3}) =

= 1- (\frac{10}{220} + \frac{4}{220} + \frac{1}{220}) = \frac{41}{44} .

Answer: D.

ARIEN3228 · Answer

Detailed Solution

Let balls are GGGGG, YYYY and WWW.

So, we could solve this question in 2 different ways:

The question can be solved by considering the two scenarios:

1) We can calculate the things that we want in above case scenarios is not the same colour.

2. The things we don't want. In this scenario we can calculate the answer (1 - we don't want ).

So, the scenarios we don't want are:

Probability of Getting a Green ball from the box = (5/12) * (4/11) * (3/10) = 60/1320

Probability of Getting Yellow ball = (4/12) * (3/11) * (2/10) = 24/1320

Probability of Getting White Ball = (3/12) * (2/11) * (1/10) = 6 /1320

So, Probability of getting Green or Yellow or White ball = (60/1320) + (24/1320) + (6/1320) = 9/132 = 3/44.

(1 - we don't want )

1- 3/44

Ans: 41/44.

ScottTargetTestPrep · Answer

The probability that, when 3 marbles are selected, they are not the same color is:

1 - P(all green or all yellow or all white)

P(all green) = 5C3/12C3 =  /(12 x 11 x 10)/3! = 10/220

P(all yellow) = 4C3/12C3 = 4/220

P(all white) = 3C3/12C3 = 1/220

Thus:

1 - (10/220 + 4/220 + 1/220) = 1 - 15/220 = 205/220 = 41/44

Answer: D

kitzi · Answer

when using the complement, do we need to also consider if the 3 marbles taken at random could have consisted of 2 marbles with same color (for example GGY, YYW, etc)?

Kunni · Answer

Hi,

How about calculating one Green, one yellow and one white

1 Green = 5/12 
1Yellow = 4/11 
1 White = 3/10

so P = (5/12)*(4/11)*(3/10) = 1/22

Bunuel · Answer

Two issues with that.

1. P(GYW) = 5/12*4/11*3/10*3!. We should multiply by 3! because GYW scenario can occur in 3! = 6 different ways: GYW, GWY, YGW, YWG, WGY, WYG, each having the probability of (5*4*3)/(12*11*10) (first is green, second is yellow, third is white, OR first is green, second is white, third is yellow, OR ...).

2. The question asks: what is the probability that they are not of the same color? This could happen also when we have two marbles of the same color and the third is of different colors. For example, GGW, GGY, YYG, YYW, WWG, WWY.

You can calculate all the above cases (in 1 and 2) and sum but it's easier to do 1 - P(opposite event), as shown in the posts above.

riagarg07 · Answer

Got your method.
But could you please tell what is wrong with my method?

I am just taking the probability of selecting 1 from each color:
(5C1*4C1*3C1)/12C3

GMATinsight · Answer

riagarg07 Your method ensures only subset of question Your method insures that all three marbles have distinct colour which is not same as all marbles should not be same color All marbes are not same color = All distinct color + 2green 1 yellow + 2 yellow 1 green + 2 white one green + 2 green 1 white + 2 yellow 1 green + 2 green 1 yellow And your method does NOT include GREEN CASES I hope that clears your doubt.

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A box contains 5 green, 4 yellow and 3 white marbles.

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