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probability that the marble selected will be purple?

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rsarashi Master | Next Rank: 500 Posts Default Avatar
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probability that the marble selected will be purple?

Post Sat Sep 02, 2017 11:49 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 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

OAC

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GMAT/MBA Expert

Post Sat Sep 02, 2017 11:59 am
rsarashi 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 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
P(marble is purple) = P(Box A is selected AND a purple ball is selected from Box A OR Box B is selected AND a purple ball is selected from Box B)
= P(Box A is selected) x P(a purple ball is selected from Box A) + P(Box B is selected) x P(a purple ball is selected from Box B)
= 1/2 x 30/50 + 1/2 x 15/50
= 3/10 + 3/20
= 6/20 + 3/20
= 9/20

Answer: C

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GMAT/MBA Expert

Post Sat Sep 02, 2017 1:25 pm
Quote:
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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