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On a store counter are exactly two boxes containing

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by canbtg » Thu Oct 31, 2013 3:10 am
On a store counter are exactly two boxes containing only purple marbles and yellow marbles.Box A has 30 purple marbles and 20 yellow marbles;box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one marble from any of the boxes ,what is the probability that the marble selected will be purple?

A)3/20
B)3/10
C)9/20
D)3/5
E)9/10

OA C[spoiler][/spoiler]
Last edited by canbtg on Thu Oct 31, 2013 3:29 am, edited 2 times in total.
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by ganeshrkamath » Thu Oct 31, 2013 3:16 am
canbtg wrote:On a store counter are exactly two boxes containing only purple marbles and yellow marbles.Box A has 30 purple marbles and 20 yellow marbles;box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one marble from that box ,what is the probability that the marble selected will be purple?

A)3/20
B)3/10
C)9/20
D)3/5
E)9/10
What do you mean by "that"?

Assuming you mean "one marble from any box":
Probability of choosing purple in Box A = 30/(30+20) = 3/5
Probability of choosing purple in Box B = 15/(15+35) = 3/10

Probability of choosing purple from either Box (assuming equal probability of choosing either box)
= 1/2 * (3/5) + 1/2 * (3/10)
= 3/10 + 3/20
= 6/20 + 3/20
= 9/20

Choose C

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by theCodeToGMAT » Thu Oct 31, 2013 3:19 am
canbtg wrote:On a store counter are exactly two boxes containing only purple marbles and yellow marbles.Box A has 30 purple marbles and 20 yellow marbles;box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one marble from that box ,what is the probability that the marble selected will be purple?

A)3/20
B)3/10
C)9/20
D)3/5
E)9/10
are you sure of the Q
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by GMATGuruNY » Thu Oct 31, 2013 6:44 am
canbtg wrote:On a store counter are exactly two boxes containing only purple marbles and yellow marbles.Box A has 30 purple marbles and 20 yellow marbles;box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one marble from any of the boxes ,what is the probability that the marble selected will be purple?

A)3/20
B)3/10
C)9/20
D)3/5
E)9/10
The two boxes are irrelevant.
Total number of purple marbles = 30+15 = 45.
Total number of marbles = 30+20+15+35 = 100.
P(purple is selected) = purple/total = 45/100 = 9/20.

The correct answer is C.
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by Brent@GMATPrepNow » Thu Oct 31, 2013 8:48 am
On a store counter are exactly two boxes containing only purple marbles and yellow marbles.Box A has 30 purple marbles and 20 yellow marbles;box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one marble from any of the boxes ,what is the probability that the marble selected will be purple?

A)3/20
B)3/10
C)9/20
D)3/5
E)9/10
Mitch's solution is definitely the best (i.e., the fastest) approach. However, I thought it might be interesting to see that we'll reach the same conclusion if we don't add all of the marbles together.

Instead, we'll keep the marbles in each box and we'll apply some probability rules involving "and" and "or".

So, P(marble is purple) = P(choose Box A and select purple OR choose Box B and select purple)
= [P(choose Box A) x P(select purple)] + [P(choose Box B) x P(select purple)]
= [1/2 x 30/50] + [1/2 x 15/50]
= 30/100 + 15/100
= 45/100
= [spoiler]9/20[/spoiler]
= C

Cheers,
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by lamania » Sun Nov 10, 2013 4:56 pm
This GMAT prep question is typed incorrectly. The question says: "If Melanie randomly selects one of the boxes and then randomly selects one marble from that box", what is the probability that the marble selected will be purpose?

I got this wrong by multiplying the probability of getting a purple marble of box A and B--3/5*3/10. What is that approach wrong? By the way, the sum of purple marbles over the total yields 9/20. That is just a coincidence, right? Or is it still the case described by Mitch in which the boxes don't matter?
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by GMATGuruNY » Sun Nov 10, 2013 5:39 pm
lamania wrote:This GMAT prep question is typed incorrectly. The question says: "If Melanie randomly selects one of the boxes and then randomly selects one marble from that box", what is the probability that the marble selected will be purpose?

I got this wrong by multiplying the probability of getting a purple marble of box A and B--3/5*3/10. What is that approach wrong? By the way, the sum of purple marbles over the total yields 9/20. That is just a coincidence, right? Or is it still the case described by Mitch in which the boxes don't matter?
The product in red would yield the correct answer to the following question:
If one marble is selected from each box, what is the probability that both of the selected marbles are purple?
P(the marble from box A is purple) = 30/50 = 3/5.
P(the marble from box B is purple) = 15/50 = 3/10.
Since we want both events to happen, we multiply the probabilities:
P(both marbles are purple) = 3/5 * 3/10 = 9/50.

In the problem at hand, only ONE marble is being selected.
As I noted above, the boxes are irrelevant.
There are a total of 100 marbles.
Of these 100 marbles, 45 are purple.
Thus:
The probability that the selected marble is purple = 45/100 = 9/20.
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