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# A certain basket contains 10 apples, 7 of which are red and

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Intern
Joined: 14 Sep 2010
Posts: 20
A certain basket contains 10 apples, 7 of which are red and  [#permalink]

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24 Jan 2011, 01:05
5
11
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:55) correct 25% (02:06) wrong based on 470 sessions

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A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 different apples are randomly selected, what is the probability that out of those 3 , 2 will be red and 1 will be green ?

A. 7/40
B. 7/20
C. 49/100
D. 21/40
E. 7/10
Math Expert
Joined: 02 Sep 2009
Posts: 49430
A certain basket contains 10 apples, 7 of which are red and  [#permalink]

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24 Jan 2011, 02:34
5
1
A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 different apples are randomly selected, what is the probability that out of those 3 , 2 will be red and 1 will be green ?

1) 7/40
2) 7/20
3) 49/100
4) 21/40
5) 7/10

Probability = # of favorable outcomes / total # of outcomes;

$$P=\frac{C^2_7*C^1_3}{C^3_{10}}=\frac{21}{40}$$, where $$C^2_7$$ is # of ways to choose 2 different green apples out of 7, $$C^1_3$$ is # of ways to choose 1 red apple out of 3, and $$C^3_{10}$$ is total # of ways to choose 3 different apples out of total 10 apples.

Or by probability approach: $$P(RRG)=\frac{3!}{2!}*\frac{7}{10}*\frac{6}{9}*\frac{3}{8}=\frac{21}{40}$$, we are multiplying by 3!/2! as the case of GGR can occur in 3 ways: GGR, GRG, RGG - # of permutation of 3 letters out of which 2 are identical.

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Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 308
Re: GMAT PREP PROBABILITY  [#permalink]

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05 Feb 2011, 07:38
4
1

probability of getting RRG

$$= \frac{7}{10}*\frac{6}{9}*\frac{3}{8} = \frac{7}{40}$$

there are 3 different ways to get 2 red and 1 green {RRG, RGR, GRR}.

so probability = $$\frac{7*3}{40} = \frac{21}{40}$$

Ans: D

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Re: A certain basket contains 10 apples, 7 of which are red and  [#permalink]

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19 Aug 2018, 01:35
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Re: A certain basket contains 10 apples, 7 of which are red and &nbs [#permalink] 19 Aug 2018, 01:35
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