Source: GMAT Prep
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 OA is C.
A basket contains 5 apples, of which 1 is spoiled and the
This topic has expert replies
-
- Moderator
- Posts: 2205
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
There are 4 good and 1 bad apple.BTGmoderatorLU wrote:Source: GMAT Prep
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 OA is C.
Probability of picking 2 apples such that 1 is good and the other is bad = (4C1 * 1C1) / (5C2) = 4/(5.4/1.2) = 2/5
The correct answer: C
Hope this helps!
-Jay
_________________
Manhattan Review GRE Prep
Locations: GRE Classes Miami | GRE Prep Course Munich | GRE Prep Denver | LSAT Prep Course Orlando | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
P(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).BTGmoderatorLU wrote:Source: GMAT Prep
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(1st apple is not spoiled) = 4/5. (Of the 5 apples, 4 are not spoiled).
P(2nd apple is not spoiled) = 3/4. (Of the 4 remaining apples, 3 are not spoiled).
Since we want both events to happen, we multiply the fractions:
4/5 * 3/4 = 3/5.
Thus, P(spoiled apple is selected) = 1 - 3/5 = 2/5.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
\[5\,\,{\text{apples}}\,\,\left\{ \begin{gathered}BTGmoderatorLU wrote:Source: GMAT Prep
A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
A. 1/5
B. 3/10
C. 2/5
D. 1/2
E. 3/5
\,1\,\,{\text{spoiled}} \hfill \\
\,4\,\,{\text{good}} \hfill \\
\end{gathered} \right.\]
\[? = P\left( {{\text{extract 2,}}\,\,{\text{1}}\,\,{\text{spoiled}}} \right)\]
\[{\text{total}}:\,\,C\left( {5,2} \right) = 10\,\,\,{\text{equiprobables}}\]
\[{\text{favorable:}}\,\,{\text{4}}\,\,\,\,\left( {{\text{spoiled}} + {\text{any}}\,\,{\text{good}}} \right)\]
\[? = \frac{4}{{10}} = \frac{2}{5}\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We need to determine the probability of selecting a spoiled apple and a non-spoiled apple when selecting two apples.BTGmoderatorLU 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 number of ways to select the spoiled apple is 1C1 = 1. The number of ways to select one 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 S-G or G-S. The probability of S-G is (1/5)(4/4) = 1/5. The probability of G-S 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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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: C
GMAT assassins aren't born, they're made,
Rich
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: C
GMAT assassins aren't born, they're made,
Rich