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

by AAPL » Sat Mar 10, 2018 5:56 am
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

The OA is D.

I solved this PS question as follow,

Total = 300

Accountants = 65

Non Accountants = 300 - 65 = 235

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

235C2/300C2 = 235 * 234 / 300 * 299 = 0.611 ~ 0.6. option D.
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by mbawisdom » Sat Mar 10, 2018 6:08 am
AAPL 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

The OA is D.

I solved this PS question as follow,

Total = 300

Accountants = 65

Non Accountants = 300 - 65 = 235

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

235C2/300C2 = 235 * 234 / 300 * 299 = 0.611 ~ 0.6. option D.
Since we are dealing with approximates I would keep the fractions approximate to save time and improve accuracy:

235/300 ~ 4/5 and 234/299 ~ 4/5

Therefore probability ~ (4/5)^2 = 16/25 ~ 0.6
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by Brent@GMATPrepNow » Mon Mar 12, 2018 7:36 am
AAPL 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
So, there are 300 employees and 235 of them are NOT accountants.

We can also 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
Brent Hanneson - Creator of GMATPrepNow.com
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by deloitte247 » Sun Mar 18, 2018 11:00 am
If 65 of the employees are accountants, then the non accountant employees are 300-65=235.
probability that the first employee selected is not an accountant $$=\frac{235}{300}\ \left[\frac{\left(number\ of\ occurence\right)}{total\ number\ of\ employee}\right]$$
$$Now,\ there\ are\ 299\ employees\ left\ out\ of\ which\ 234\ are\ non\ accoun\tan ts.$$
probability of selecting another non-accountant is =234/299

Therefore, the probability that the two employees chosen are not accountants= $$\frac{235}{300}\cdot\frac{234}{299}$$
= $$0.78333\cdot0.78261$$
= $$0.613\ =0.6\ \left(option\ D\right)$$
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by Scott@TargetTestPrep » Sun Jun 02, 2019 4:19 pm
AAPL 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
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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