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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
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Number of non-accountants = 300 -65 = 235

Probability that neither is an accountant = 235C2 / 300C2
= 0.6 (approx)


Answer : D

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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
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Bunuel wrote:
Of the 300 employees of a certain company, 65 are accountants. Two employees of the company will be selected at random. Which of the following is closest to the probability that neither of the employees selected will be an accountant?

A 0.3
B 0.4
C 0.5
D 0.6
E 0.7

Kudos for a correct solution.


Ans: D

We can Solve this by two ways:
either find the probability by = 1-(both accountant+atleast one accountant)
or direct from = P(both non accountant)

second is easier but requires calculation if don't do the approximation.
So probability= (235/300)*(234/299) = 0.61
so the answer is D
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
1
Kudos
Total = 300
Accountants = 65
Non Accountants = 300 - 65= 235

Two employees of the company will be selected at random so probability that neither of the employees selected will be an accountant is

235 C 2 / 300 C 2 = 235 * 234 / 300 * 299 = 0.611 ~ 0.6

Hence D 0.6 is the correct answer
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
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Bunuel wrote:
Of the 300 employees of a certain company, 65 are accountants. Two employees of the company will be selected at random. Which of the following is closest to the probability that neither of the employees selected will be an accountant?

A 0.3
B 0.4
C 0.5
D 0.6
E 0.7

Kudos for a correct solution.


The probability that two randomly selected employees will not be an accountant is 235/300 x 234/299. We can round this to:

235/300 x 235/300 = 47/60 x 47/60 ≈ 45/60 x 50/60 = 3/4 x 5/6 = 5/8 ≈ 0.6

Answer: D
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
Expert Reply
Total: 300

To be selected (2): \(^{300}{C_2} = 150 * 299\)

Accountant: 65
Non- Accountant: 235

To be selected (2) non-accountant: \(^{235}{C_2} = 235 * 117\)

Probability: \(\frac{235 * 117 }{ 150 * 299} = \frac{240 * 120 }{ 150 * 300} = 0.6 (0.64)\)

Answer D
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
Hi MathRevolution and bb
This question is actually pretty decent to solve but I am studying in a group with a bunch of other GMAT Aspirants and we all have a common query.
In this case we took 235/300 * 234/299 i.e. No repetition.
But can you compile what we do when nothing is stated regarding the repetition (Like in this case, I did (235*300)^2 and got 0.6 - the correct answer)
Briefly, can you explain what to do regarding repetition and non repetition in cases when question doesn't state anything explicitly.
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
Expert Reply
KabxW wrote:
Hi MathRevolution and bb
This question is actually pretty decent to solve but I am studying in a group with a bunch of other GMAT Aspirants and we all have a common query.
In this case we took 235/300 * 234/299 i.e. No repetition.
But can you compile what we do when nothing is stated regarding the repetition (Like in this case, I did (235*300)^2 and got 0.6 - the correct answer)
Briefly, can you explain what to do regarding repetition and non repetition in cases when question doesn't state anything explicitly.


If I understand you correctly you are confused about "with replacement"/"without replacement" rather than "repetition". I agree that the question should be clearer and state that the selection is maned without replacement. Edited to avoid confusion.
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
Expert Reply
KabxW wrote:
Hi MathRevolution and bb
This question is actually pretty decent to solve but I am studying in a group with a bunch of other GMAT Aspirants and we all have a common query.
In this case we took 235/300 * 234/299 i.e. No repetition.
But can you compile what we do when nothing is stated regarding the repetition (Like in this case, I did (235*300)^2 and got 0.6 - the correct answer)
Briefly, can you explain what to do regarding repetition and non repetition in cases when question doesn't state anything explicitly.



Hello,

"Without replacement" - the term is always mentioned in the problem statement.

Also, \(\frac{235 }{ 300}\) is 0.78 so if you square you will get 0.6xx

On the other hand, \(\frac{234 }{ 299}\) is also 0.78 so if you do \(\frac{235}{300}\) * \(\frac{234}{299} \)= 0.78 * 0.78 = 06xxxx

But say there were 10 balls and we have to pick 2 without replacement, then \(\frac{1}{10}\) * \(\frac{1}{9}\) will not be same as \((\frac{1}{10})^2\).

Thanks
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
Expert Reply
Of the 300 employees at a certain company, 65 are accountants. If two employees are selected at random without replacement, which of the following most closely represents the probability that neither selected employee is an accountant?

A. 0.3
B. 0.4
C. 0.5
D. 0.6
E. 0.7


There are 300 - 65 = 235 employees who are NOT accountants. Therefore, the probability that neither of the two selected employees is an accountant is:

\(P = \frac{235}{300}*\frac{234}{299} \approx{\frac{240}{300}*\frac{240}{300} } = 0.8*0.8=0.64\).


Answer: D
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
Given: Of the 300 employees at a certain company, 65 are accountants.

Asked: If two employees are selected at random without replacement, which of the following most closely represents the probability that neither selected employee is an accountant?

Total ways to select 2 employee without replacement = 300C2 = 300*299/2
Ways in which that neither selected employee is an accountant = (300-65)(299-65)/2 = 235*234/2

The probability that neither selected employee is an accountant = 235*234/300*299 = 0.6

IMO D
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Re: Of the 300 employees at a certain company, 65 are accountants. If two [#permalink]
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