Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 03 Feb 2009
Posts: 16
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins

A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
02 Mar 2009, 11:37
Question Stats:
73% (01:24) correct 27% (01:33) wrong based on 1006 sessions
HideShow timer Statistics
A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple? A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 61283

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
18 Nov 2010, 11:34
A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5 Direct combinatorial approach:\(Probability=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}\): Favorable outcomes: \(C^1_1*C^1_4\) > \(C^1_1\) choosing one rotten out of 1 and \(C^1_4\) choosing any for the second apple; Total # of outcomes: \(C^2_5\), choosing 2 apples out of 5; \(P=\frac{C^1_1*C^1_4}{C^2_5}=\frac{2}{5}\). Reverse combinatorial approach:Let's count the probability of the opposite event and subtract this value from 1. The opposit event will be if out of 2 apples both are good, so \(P=1\frac{C^2_4}{C^2_5}=\frac{2}{5}\). Direct probability approach:\(P=\frac{1}{5}*\frac{4}{4}+\frac{4}{5}*\frac{1}{4}=\frac{2}{5}\): probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}. Reverse probability approach:Again 1 the probability of the opposite event > \(P=1\frac{4}{5}*\frac{3}{4}=\frac{2}{5}\). Answer: C.Check Probability chapter of Math Book for more on this issues: http://gmatclub.com/forum/mathprobability87244.htmlHope it helps.
_________________




Intern
Joined: 16 Feb 2009
Posts: 47
Schools: Anderson FEMBA

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
02 Mar 2009, 13:46
Total Apples = 5 Spoiled Apples = 1 Not Spoiled Apples = 4
Possible outcomes: (Apple 1) Not Spoiled, (Apple 2) Spoiled; = (4/5)*(1/4) = 4/20 or 2/10. OR (Apple 1) Spoiled, (Apple 2) Not Spoiled; = (1/5)*(4/4) = 4/20 or 2/10.
Total Probability = 2/10 + 2/10 = 4/10 or 2/5.




VP
Joined: 07 Nov 2007
Posts: 1102
Location: New York

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
02 Mar 2009, 13:22
bmiller0731 wrote: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
a) 1/5 b) 3/10 c) 2/5 d) 1/2 e) 3/5 p (both apples are not spoiled) = 4C2/5C2 = 4*3/5*4 = 3/5 p (one of the apple spoiled) = 13/5 = 2/5



Intern
Joined: 18 Nov 2010
Posts: 8

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
18 Nov 2010, 11:08
A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?
A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5



Intern
Joined: 18 Nov 2010
Posts: 8

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
18 Nov 2010, 11:47
This is the best explanation on probability I have ever got = using all the approaches. Thanks! I now know how Combinations/Direct Probability etc. all tie together!



Senior Manager
Joined: 25 May 2010
Posts: 283
Location: United States
Concentration: Strategy, Finance
GMAT 1: 590 Q47 V25 GMAT 2: 560 Q47 V20 GMAT 3: 600 Q47 V25 GMAT 4: 680 Q49 V34

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
18 Nov 2010, 15:52
@ Bunuel, you're awesome. Do you focus on anything else apart form solving Quant questions on GC?:) Just kidding. Kudos +1..
_________________
"Whether You Think You Can or Can't, You're Right"Henry Ford 680 Debrief600 Debrief590 DebriefMy GMAT Journey



Math Expert
Joined: 02 Sep 2009
Posts: 61283

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
25 Mar 2012, 11:12
21. Combinatorics/Counting Methods For more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



Manager
Joined: 15 Apr 2011
Posts: 58

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
25 Mar 2012, 20:42
Bunuel, you are awesome!
_________________
http://mymbadreamz.blogspot.com



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 892
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
27 Aug 2012, 10:52
+1 C Total number of combinations: 5!/3! = 20 Number of combinations that include the spoiled apple: When the spoiled apple is the first apple picked: 1*4= 4 When the spoiled apple is the second apple picked: 4*1 = 4 Total: 8 Probability: 8/20 = 2/5 C.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html GMAT Club Premium Membership  big benefits and savings



Director
Joined: 22 Mar 2011
Posts: 583
WE: Science (Education)

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
27 Aug 2012, 13:09
bmiller0731 wrote: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5 Computing directly probabilities and using the complementary event: P(spoiled apple selected) = 1  P(no spoiled apple selected) = 1  P(first apple not spoiled)*P(second apple also not spoiled) = 1  (4/5)*(3/4) = 1  3/5 = 2/5. Answer C
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Current Student
Joined: 03 Sep 2012
Posts: 366
Location: United States
Concentration: Healthcare, Strategy
GPA: 3.88
WE: Medicine and Health (Health Care)

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
25 Sep 2012, 08:37
No. of apples that are not spoiled = 4 No. of apples that are spoiled = 1 The question is asking us to find out the probability of finding one spoiled apple among the 2 randomly selection ... We can have 2 scenarios , Scenario A) where the first apple selected is not spoiled , and the second apple selected is spoiled and Scenario B) where the first apple selected is spoiled and the second selected is not spoiled .. Scenario A) We have four apples out of five that are not spoiled , therefore probability is 4/5 , the second apple is a spoiled one out of the remaining 4 , therefore we have overall probability of this outcome as (4/5) x (1/4) = 4/20 Scenario B ) We have only one apple out of 5 that is spoiled so probability is 1/5 , the second apple can be one from any 4 remaining thefore 4/4... Probability of this outcome is (1/5) x (4/4) = 1/5 .... We must add these two scenarios therefore we get 4/20 + 1/5 = 8/20 = 2/5 (C)
_________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.”  Eric Thomas



Senior Manager
Joined: 13 Aug 2012
Posts: 393
Concentration: Marketing, Finance
GPA: 3.23

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
26 Sep 2012, 02:21
Anagram helps.
Attachments
Selecting 2 from 5 apples.jpg [ 26.71 KiB  Viewed 55627 times ]



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9426
Location: United States (CA)

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
16 Jul 2017, 16:32
bmiller0731 wrote: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5 We need to determine the probability of selecting a spoiled apple and a nonspoiled apple when selecting two apples. The number of ways to select the spoiled apple is 1C1 = 1. The number of ways to select a good apple is 4C1 = 4. Thus, the spoiled apple and a good apple can be selected in 1 x 4 = 4 ways. The number of ways to select 2 apples from 5 is 5C2 = (5 x 4)/2! = 20/2 = 10. Thus, the probability of selecting the spoiled apple and a good apple is 4/10 = 2/5. Alternate Solution: There are two outcomes that satisfy the requirement that the spoiled apple (S) is chosen along with a good apple (G), either SG or GS. The probability of SG is (1/5)(4/4) = 1/5. The probability of GS is (4/5)(1/4) = 1/5. Since either outcome satisfies our requirement, we add these two probabilities: 1/5 + 1/5 = 2/5. Answer: C
_________________
5star 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.



Manager
Joined: 02 Jan 2017
Posts: 67
Location: Pakistan
Concentration: Finance, Technology
GPA: 3.41
WE: Business Development (Accounting)

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
22 Dec 2017, 05:25
Good Apple= A Spoiled Apple = S
Total ways of selecting two appls = ( A * S) + ( S*S)
What i want to ask is why are we not consideringt the order of selection here. For example ( A*S) could also be taken as ( S*A). Why is the order not improtant here?
Is it because the word [ Selection ] has been mentioned and that makes this a combination question?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16107
Location: United States (CA)

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
07 Apr 2018, 09:36
Hi All We're told that we have 4 regular apples and 1 spoiled apple. We're asked  if you grab 2 apples, then what's the probability of getting the spoiled apple? The question can be solved in a couple of ways. Here's how to track each of the different outcomes that matches what we're looking for: 1st regular, 2nd spoiled = (4/5)(1/4) = 4/20 1st spoiled, 2nd regular = (1/5)(4/4) = 4/20 Total ways to get 1 spoiled and 1 regular = 4/20 + 4/20 = 8/20 = 2/5 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4324
Location: Canada

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
15 Sep 2018, 05:35
bmiller0731 wrote: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5 The two approaches shown above are the best (faster) approaches, but here's one more. Since there are so few objects involved (5 apples), we should be able to quickly answer the question by simply listing and counting Let A, B, C, D, and E represent the 5 apples, and let E represent the SPOILED APPLEWe want to select 2 apples at random. So, let's list all of the possible outcomes: 1) AB 2) AC 3) AD 4) A E5) BC 6) BD 7) B E8) CD 9) C E10) D ESo, there are 10 possible outcomes Of those 10 possible outcomes, 4 outcomes include the SPOILED APPLESo, P(selection includes the spoiled apple) = 4/ 10 = 2/5 Answer: C Cheers, Brent
_________________
Test confidently with gmatprepnow.com



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
15 Sep 2018, 17:06
bmiller0731 wrote: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5
\(5\,\,{\text{apples}}\,\,\left\{ \begin{gathered} \,1\,\,{\text{spoiled}} \hfill \\ \,4\,\,{\text{good}} \hfill \\ \end{gathered} \right.\) \(? = P\left( {{\text{extract 2,}}\,\,{\text{1}}\,\,{\text{spoiled}}} \right)\) \({\text{total}}:\,\,C\left( {5,2} \right) = 10\,\,\,{\text{equiprobables}}\) \({\text{favorable:}}\,\,{\text{4}}\,\,\,\,\left( {{\text{spoiled}} + {\text{any}}\,\,{\text{good}}} \right)\) \(? = \frac{4}{{10}} = \frac{2}{5}\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 21 Nov 2018
Posts: 14
Location: Nigeria
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Analyst (Investment Banking)

Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
Show Tags
12 Oct 2019, 08:03
Bunuel wrote: A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?A. 1/5 B. 3/10 C. 2/5 D. 1/2 E. 3/5 Direct combinatorial approach:\(Probability=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}\): Favorable outcomes: \(C^1_1*C^1_4\) > \(C^1_1\) choosing one rotten out of 1 and \(C^1_4\) choosing any for the second apple; Total # of outcomes: \(C^2_5\), choosing 2 apples out of 5; \(P=\frac{C^1_1*C^1_4}{C^2_5}=\frac{2}{5}\). Reverse combinatorial approach:Let's count the probability of the opposite event and subtract this value from 1. The opposit event will be if out of 2 apples both are good, so \(P=1\frac{C^2_4}{C^2_5}=\frac{2}{5}\). Direct probability approach:\(P=\frac{1}{5}*\frac{4}{4}+\frac{4}{5}*\frac{1}{4}=\frac{2}{5}\): probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}. Reverse probability approach:Again 1 the probability of the opposite event > \(P=1\frac{4}{5}*\frac{3}{4}=\frac{2}{5}\). Answer: C.Check Probability chapter of Math Book for more on this issues: http://gmatclub.com/forum/mathprobability87244.htmlHope it helps. P=15∗44+45∗14=25P=15∗44+45∗14=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}. Hello BunuelWhy are we considering the order of selection here....when do we know to consider order and when not too? Thanks




Re: A basket contains 5 apples, of which 1 is spoiled and the rest are
[#permalink]
12 Oct 2019, 08:03






