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

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

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