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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, 01:28
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5% (low)

Question Stats:

82% (01:24) correct 18% (01:34) wrong based on 93 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. $$\frac{1}{7}$$

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1355 Location: Viet Nam Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink] ### Show Tags 07 Aug 2017, 05:58 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 The answer is C _________________ Manager Joined: 06 Jul 2014 Posts: 94 Location: India Concentration: Finance, Entrepreneurship GMAT 1: 660 Q48 V32 Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink] ### Show Tags 07 Aug 2017, 06:08 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. Intern Joined: 15 Mar 2017 Posts: 38 Location: India Concentration: International Business, Strategy GMAT 1: 720 Q50 V37 GPA: 4 Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink] ### Show Tags 07 Aug 2017, 07:57 1 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 Please hit kudos if my answer helped. _________________ You give kudos, you get kudos. :D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7101 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. [#permalink] ### Show Tags 09 Aug 2017, 18:08 ==> 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. The answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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, 10:30
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]

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25 Feb 2019, 20:28
Since the total countable items is 5 . As there exists 4 good and 1 rotten apples . simply at once the selection of apples will have 1 good and 1 rotten apple.

As probability is defined as favorable outcomes / total outcomes . Answer is 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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02 Mar 2019, 10:10
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 2 apples consisting of 1 good apple and 1 rotten apple is selected is 4C1 x 1C1 = 4 x 1 = 4.

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

So the probability is 4/10 = 2/5.

Alternate Solution:

There are two ways to get 1 good and 1 bad apple in this scenario: GB or BG

The probability of GB is 4/5 x 1/4 = 1/5

The probability of BG is 1/5 x 4/4 = 1/5

Since either outcome satisfies the requirement, we add the two probabilities, obtaining 1/5 + 1/5 = 2/5.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten.   [#permalink] 02 Mar 2019, 10:10
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