Probability from GMAT prep

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jkelk: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Mon Mar 12, 2012 3:05 am

by jkelk » Mon Mar 12, 2012 3:08 am

A basket contains 5 apples of which 1 is spolied & the rest are good. If henry is to select 2 apples from the basket simultaneously & at random, what is the probability 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

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 12, 2012 3:47 am

jkelk wrote:A basket contains 5 apples of which 1 is spolied & the rest are good. If henry is to select 2 apples from the basket simultaneously & at random, what is the probability 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(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).

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.

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killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Mon Mar 12, 2012 3:55 am

GMATGuruNY wrote:
jkelk wrote:A basket contains 5 apples of which 1 is spolied & the rest are good. If henry is to select 2 apples from the basket simultaneously & at random, what is the probability 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(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).

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.

Hey Mitch,

Whats the significance of the word "simultaneous" used here?
doesnt it mean we cant calculate by picking one apple then other (please explain the part in bold)

thanx

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 12, 2012 4:03 am

killer1387 wrote:
GMATGuruNY wrote:
jkelk wrote:A basket contains 5 apples of which 1 is spolied & the rest are good. If henry is to select 2 apples from the basket simultaneously & at random, what is the probability 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(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).

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.
Hey Mitch,

Whats the significance of the word "simultaneous" used here?
doesnt it mean we cant calculate by picking one apple then other (please explain the part in bold)

thanx

The probability of picking the apples SIMULTANEOUSLY is no different from the probability of picking the apples WITHOUT REPLACEMENT.
Both wordings convey the same restriction: each apple can be selected ONLY ONCE. Once an apple has been selected, it cannot be selected again.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 15, 2018 5:33 am

jkelk wrote:A basket contains 5 apples of which 1 is spolied & the rest are good. If henry is to select 2 apples from the basket simultaneously & at random, what is the probability 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 APPLE

We want to select 2 apples at random. So, let's list all of the possible outcomes:
1) AB
2) AC
3) AD
4) AE
5) BC
6) BD
7) BE
8) CD
9) CE
10) DE

So, there are 10 possible outcomes
Of those 10 possible outcomes, 4 outcomes include the SPOILED APPLE

So, P(selection includes the spoiled apple) = 4/10 = 2/5

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sat Sep 15, 2018 5:02 pm

jkelk 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. 1/5
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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8178; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 10, 2019 4:56 pm

jkelk wrote:A basket contains 5 apples of which 1 is spolied & the rest are good. If henry is to select 2 apples from the basket simultaneously & at random, what is the probability 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 non-spoiled apple when selecting two apples.

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.

Alternate Solution:

Let's first determine the event that the selection does not include the spoiled apple. Since there are 4 good apples among a total of 5 apples, the probability that the first apple is good is 4/5 and the probability that the second apple is good is 3/4. Thus, the probability that the selection does not contain the spoiled apple is 4/5 x 3/4 = 3/5.

Since the event that the selection contains the spoiled apple and the event that the selection does not contain the spoiled apple are complementary event, the probability that the selection contains the spoiled apple is 1 - 3/5 = 2/5.

Answer: C

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