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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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15% (low)

Question Stats:

78% (01:27) correct 22% (01:45) wrong based on 139 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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1333 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 1 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: 88 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: 8001 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$79 for 1 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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# Scott Woodbury-Stewart

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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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 30 May 2019
Posts: 2
Re: There are 5 apples in a bag. 4 apples are good but 1 apple is rotten.  [#permalink]

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24 Jun 2019, 08:59
Hi, I was wandering if the approach of "1 - counterprobability ( =no rotten apple)" is valid? I.e. 1 - 4/5*3/4= 1 - 12/20= 8/20 = 2/5
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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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24 Jun 2019, 09:49
1
max96hsv wrote:
Hi, I was wandering if the approach of "1 - counterprobability ( =no rotten apple)" is valid? I.e. 1 - 4/5*3/4= 1 - 12/20= 8/20 = 2/5

Yes! Great and totally valid solution. While this method is most commonly used with more complex "at least/more than" problems, any time we can break the scenario down into complementary events (two events where one and only one event must occur), we can solve for one event by finding 1 - the probability of its complement.

In this case, the complement of picking the bad apple is NOT picking the bad apple, so the probability of picking the bad apple = 1 - the probability of NOT picking the bad apple.

On the first pick, we have a 4/5 chance of NOT picking the bad apple (out of the 5 total apples in the bag, 4 are NOT bad). On the second pick, we have a 3/4 chance of NOT picking the bad apple (of the 4 apples left in the bag after the first pick, 3 are NOT bad). So we have a 4/5*3/4 = 12/20 = 3/5 chance of NOT picking the bad apple in either of the two picks. So the chance of picking the bad apple in either of the two picks is 1 - 3/5 = 2/5.
There are 5 apples in a bag. 4 apples are good but 1 apple is rotten.   [#permalink] 24 Jun 2019, 09:49
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