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Probability from GMAT prep

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Probability from GMAT prep

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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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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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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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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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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

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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.

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