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
Probability from GMAT prep
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P(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).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(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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Hey Mitch,GMATGuruNY wrote:P(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).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(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.
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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The probability of picking the apples SIMULTANEOUSLY is no different from the probability of picking the apples WITHOUT REPLACEMENT.killer1387 wrote:Hey Mitch,GMATGuruNY wrote:P(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected).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(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.
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
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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As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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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.
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As a tutor, I don't simply teach you how I would approach problems.
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The two approaches shown above are the best (faster) approaches, but here's one more.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
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
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\[5\,\,{\text{apples}}\,\,\left\{ \begin{gathered}jkelk wrote:A basket contains 5 apples of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
A. 1/5
B. 3/10
C. 2/5
D. 1/2
E 3/5
\,1\,\,{\text{spoiled}} \hfill \\
\,4\,\,{\text{good}} \hfill \\
\end{gathered} \right.\]
\[? = P\left( {{\text{extract 2,}}\,\,{\text{1}}\,\,{\text{spoiled}}} \right)\]
\[{\text{total}}:\,\,C\left( {5,2} \right) = 10\,\,\,{\text{equiprobables}}\]
\[{\text{favorable:}}\,\,{\text{4}}\,\,\,\,\left( {{\text{spoiled}} + {\text{any}}\,\,{\text{good}}} \right)\]
\[? = \frac{4}{{10}} = \frac{2}{5}\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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We need to determine the probability of selecting a spoiled apple and a non-spoiled apple when selecting two apples.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 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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