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Of the 300 employees of a certain company, 65 are accountants. Two emp

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Of the 300 employees of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 11 May 2015, 07:58
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Question Stats:

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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

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Re: Of the 300 employees of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 11 May 2015, 09:44
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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 of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 11 May 2015, 21:26
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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.
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Re: Of the 300 employees of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 11 May 2015, 22:09
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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 of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 11 May 2015, 22:32
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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 of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 18 May 2015, 05:44
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.


OFFICIAL SOLUTION:

There are 300 - 65 = 235 employees who are NOT accountants. Therefore, the probability that neither of the two employees selected being an accountant is:
P = 235/300*234/299 = ~0.8*0.8 = 0.64.

Answer: D.
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Re: Of the 300 employees of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 12 Mar 2018, 08:40
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Top Contributor
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.


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
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Re: Of the 300 employees of a certain company, 65 are accountants. Two emp  [#permalink]

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New post 02 Jun 2019, 17:30
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 of a certain company, 65 are accountants. Two emp   [#permalink] 02 Jun 2019, 17:30
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