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Probability

by Sak32 » Sat Jan 25, 2014 6:07 am
On a store counter are exactly 2 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 of the boxes and then 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

Source material: GMAT prep.Please provide explanations. Thank you.
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by bubbliiiiiiii » Sat Jan 25, 2014 7:24 am
Sak32 wrote:On a store counter are exactly 2 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 of the boxes and then 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

Source material: GMAT prep.Please provide explanations. Thank you.
Probability of selecting a purple marble from Box A = 3/5
Probability of selecting a purple marble from Box B = 3/10

Probability of selecting a purple marble from either of the boxes is 3/5 + 3/10

= 3(2++1)/10

= 9/10
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Pranay
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by Brent@GMATPrepNow » Sat Jan 25, 2014 7:31 am
Sak32 wrote:On a store counter are exactly 2 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 of the boxes and then 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
Since Melanie can choose a marble from EITHER box, the fact that the marbles are in two different boxes is irrelevant.

There are 100 marbles altogether (30 + 20 + 15 + 35 = 100)
Of those 100 marbles, 45 are purple (30 + 15 = 45)

So, P(select purple marble) = 45/100 = [spoiler]9/20 = C[/spoiler]

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Brent
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by Brent@GMATPrepNow » Sat Jan 25, 2014 7:32 am
Sak32 wrote:On a store counter are exactly 2 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 of the boxes and then 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
Another (longer) approach, is to keep the marbles in each box and 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,
Brent
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by bubbliiiiiiii » Sat Jan 25, 2014 7:53 am
Thanks sir for the correction. I thought since marble can be picked from either box then we don't have to calculate the probability of selecting each box because anyways we use an OR relation between the two boxes.
Regards,

Pranay
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