A basket contains 5 apples, of which 1 is spoiled and the : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 Feb 2017, 19:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A basket contains 5 apples, of which 1 is spoiled and the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Feb 2009
Posts: 27
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
Followers: 0

Kudos [?]: 18 [0], given: 0

A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

02 Mar 2009, 11:37
13
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:47) correct 30% (00:52) wrong based on 718 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
[Reveal] Spoiler: OA
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 35

Kudos [?]: 879 [3] , given: 5

### Show Tags

02 Mar 2009, 13:22
3
KUDOS
3
This post was
BOOKMARKED
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) = 1-3/5 = 2/5
_________________

Smiling wins more friends than frowning

Manager
Joined: 16 Feb 2009
Posts: 56
Schools: Anderson FEMBA
Followers: 1

Kudos [?]: 105 [8] , given: 1

### Show Tags

02 Mar 2009, 13:46
8
KUDOS
1
This post was
BOOKMARKED
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.
Senior Manager
Joined: 24 Feb 2007
Posts: 265
Location: nj
Followers: 1

Kudos [?]: 252 [0], given: 2

### Show Tags

07 Mar 2009, 09:41
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 = 4/5*1/4 + 1/5*4/4 = 2/5
Manager
Joined: 26 Dec 2008
Posts: 58
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
Followers: 2

Kudos [?]: 12 [0], given: 0

### Show Tags

07 Mar 2009, 09:58
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

prob (one spoiled and one good) = (no. of ways of selecting 1 spoiled and 1 good)/(total no. of ways of selecting 2 apples)

prob = (select one good AND one bad)/(select any two out of 5) = 4c1*1C1 / 5c2 = 2/5
Manager
Joined: 15 Apr 2011
Posts: 70
Followers: 0

Kudos [?]: 17 [0], given: 45

### Show Tags

25 Mar 2012, 08:45
I didn't understand. Could someone explain?
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7244

Kudos [?]: 96345 [12] , given: 10737

A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

25 Mar 2012, 11:12
12
KUDOS
Expert's post
11
This post was
BOOKMARKED
I didn't understand. Could someone explain?

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

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 --> $$P=1-\frac{4}{5}*\frac{3}{4}=\frac{2}{5}$$.

Check Probability chapter of Math Book for more on this issues: math-probability-87244.html

Hope it helps.
_________________
Manager
Joined: 15 Apr 2011
Posts: 70
Followers: 0

Kudos [?]: 17 [0], given: 45

Re: A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

25 Mar 2012, 20:42
Bunuel, you are awesome!
_________________

Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1713
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 101

Kudos [?]: 940 [0], given: 109

Re: A basket contains 5 apples, of which 1 is spoiled and the [#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/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 910 [0], given: 43

Re: A basket contains 5 apples, of which 1 is spoiled and the [#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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 03 Sep 2012
Posts: 338
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 16

Kudos [?]: 183 [1] , given: 31

Re: A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

25 Sep 2012, 08:37
1
KUDOS
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: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 26

Kudos [?]: 443 [0], given: 11

### Show Tags

26 Sep 2012, 02:21
Anagram helps.
Attachments

Selecting 2 from 5 apples.jpg [ 26.71 KiB | Viewed 17495 times ]

_________________

Impossible is nothing to God.

Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7244

Kudos [?]: 96345 [0], given: 10737

Re: A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

26 Aug 2013, 06:01
Bumping for review and further discussion.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13924
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

28 Sep 2014, 07:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 16 Nov 2013
Posts: 29
Followers: 0

Kudos [?]: 17 [0], given: 3

A basket contains 5 apples, of which 1 is spoiled and the rest [#permalink]

### Show Tags

13 Feb 2015, 02:45
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 probability that the 2 apples selected will include the spoiled apple?

A 1/20

B 1/10

C 1/5

D 2/5

E 3/5

Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7244

Kudos [?]: 96345 [0], given: 10737

Re: A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

13 Feb 2015, 02:53
gmatmania17 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 probability that the 2 apples selected will include the spoiled apple?

A 1/20

B 1/10

C 1/5

D 2/5

E 3/5

Merging topics.

Please search before posting and tag the questions properly. Thank you.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13924
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: A basket contains 5 apples, of which 1 is spoiled and the [#permalink]

### Show Tags

21 Jun 2016, 08:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A basket contains 5 apples, of which 1 is spoiled and the   [#permalink] 21 Jun 2016, 08:27
Similar topics Replies Last post
Similar
Topics:
10 A box contains 10 apples. 9 of which are red. An apple is drawn... 3 19 Aug 2016, 09:16
2 There are 6 baskets numbered from 1 to 6 and filled with apples 2 24 Feb 2016, 19:21
A crate of apples contains 1 bruised apple for every 30 apples in the 2 13 Dec 2015, 04:03
13 A certain basket contains 10 apples, 7 of which are red and 4 24 Jan 2011, 00:05
9 A basket contains 5 apples of which one is rotten. If Henry 5 18 Nov 2010, 11:08
Display posts from previous: Sort by

# A basket contains 5 apples, of which 1 is spoiled and the

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.