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# There are 5 apples in a bag. 4 apples are good but 1 apple is rotten.

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Math Revolution GMAT Instructor
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There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink]

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07 Aug 2017, 00:28
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Question Stats:

79% (00:43) correct 21% (00:40) wrong based on 77 sessions

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There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. If you take out 2 apples from the bag, what is the probability that 1 apple selected is rotten?

A. $$\frac{1}{3}$$

B. $$\frac{1}{4}$$

C. $$\frac{2}{5}$$

D. $$\frac{3}{5}$$

E. $$\frac{1}{7}$$
[Reveal] Spoiler: OA

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Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink]

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07 Aug 2017, 04:58
MathRevolution wrote:
There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. If you take out 2 apples from the bag, what is the probability that 1 apple selected is rotten?

A. $$\frac{1}{3}$$

B. $$\frac{1}{4}$$

C. $$\frac{2}{5}$$

D. $$\frac{3}{5}$$

E. $$\frac{1}{7}$$

Select 2 apples from 5 apples, there are totally 5C2 = 10 selections.

Select 2 apples that is good from 5 apples, there are totally 4C2 = 6 selections.

The probability that select 2 apples from 5 apples, there is one rotten apple, is: 1 - 6/10 = 4/10 = 2/5

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Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink]

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07 Aug 2017, 05:08
Out of 4 good apples 1 good apple can be chosen in 4 ways and 1 rotten apple can be chosen in one way. Therefore total number of favourable ways= 4. Total number of possible ways=10. Thus C.

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Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink]

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07 Aug 2017, 06:57
Another way can be by making 2 cases

1st case
1st apple to be picked up is rotten, 2nd is not:

1/5*4/4

2nd case

1st apple to be picked up is not rotten, 2nd is rotten:

4/5*1/4

Adding both the cases we get 2/5

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Math Revolution GMAT Instructor
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Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink]

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09 Aug 2017, 17:08
==> From probability=want/total, want=selecting one rotten apple and one good apple, and total=selecting 2 of 4 apples, so you get
probability=4C1*1C1/5C2=(4)(1)/(5*4/2!)=4/10=2/5.

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Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink]

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10 Aug 2017, 09:30
MathRevolution wrote:
There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. If you take out 2 apples from the bag, what is the probability that 1 apple selected is rotten?

A. $$\frac{1}{3}$$

B. $$\frac{1}{4}$$

C. $$\frac{2}{5}$$

D. $$\frac{3}{5}$$

E. $$\frac{1}{7}$$

The number of ways to select the one rotten apple is 1C1 = 1. The number of ways to select 1 good apple is 4C1 = 4, so the total number of ways to select the 2 apples with one of them rotten is 1 x 4 = 4.

The number of ways to select 2 apples from 5 is 5C2 = (5 x 4)/2! = 10.

So, the probability of selecting 2 apples with one of them rotten is 4/10 = 2/5.

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Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten.   [#permalink] 10 Aug 2017, 09:30
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