Of the 300 employees at a certain company, 65 are accountants. If two

Question

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

bluesquare · Accepted Answer

65 accountants -> 235 non accountants.
Probability of selecting 2 non accountants = 235/300*234/299, but because we are looking for an approximation, we can just do 235/300*235/300 => (divide each side by 3) 78.333/100*78.333*100 -> round to 78*78/10000. 78*78 is easy to do on paper (6084), so the answer is 6084/10000, or ~60%, which is D.

BrentGMATPrepNow · Answer

So, there are 300 employees and 235 of them are NOT accountants.

We can solve the question by applying  probability rules

P(neither selection is an accountant) = P(1st selection is not an accountant   AND   2nd selection is not an accountant)
= P(1st selection is not an accountant)   x   P(2nd selection is not an accountant)
= 235/300   x   234/299

IMPORTANT: evaluating this product is a pain. Since the answer choices are reasonably spread apart, we can use   estimation  
Notice that 235/300 is a little bit less than 240/300 (aka 0.8).
In other words, 235/300 is  a little bit less than 0.8 
Likewise, 234/299 is  a little bit less than 0.8

235/300   x   234/299 ≈ ( a little bit less than 0.8 )   x   ( a little bit less than 0.8 )
≈  a little bit less than 0.64  
So, the BEST answer is D

ASIDE: After the first non-accountant is selected, there are 299 employees remaining and there are 234 non-accountants remaining. So,P(2nd selection is not an accountant) = 234/299

Cheers,
Brent

askhere · Answer

Number of non-accountants = 300 -65 = 235

Probability that neither is an accountant = 235C 2  / 300C 2 
 = 0.6 (approx)

Answer :  D

Ambarish

D3N0 · Answer

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

cutegirlsimran · Answer

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

ScottTargetTestPrep · Answer

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

MathRevolution · Answer

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

KabxW · Answer

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.

Bunuel · Answer

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.

MathRevolution · Answer

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

Bunuel · Answer

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

Kinshook · Answer

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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Of the 300 employees at a certain company, 65 are accountants. If two

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