A very large company has equal amounts of male and female employees. If a random sample of four employees is selected, what is the probability that all four employees selected are female? A) 0.0256 B) 0.0625. C) 0.1600 D) 1.0000 Your answer: A was incorrect. The correct answer was B) 0.0625. Each employee has equal chance of being male or female. Hence, probability of 4 “successes” = (0.5)4 = 0.0625 Their answer is only correct if the random sample can include the same employee more than once (which doesn’t make sense logically). Since it doesn’t explicitly say that, there’s no way to know whether you should remove an employee from the list of potential employees to be selected once they have been chosen. For example, if a female was selected, that would decrease the female population by 1 and increase the chance of a male to be selected on the next pick. Their criteria for selection is ambiguous.

What’s the value if we assume company population is 10,000?

I think that “A very large company” is the key here. If a company has 100,000 men and 100,000 women… adjusting the calculation would result in an immaterial difference. Techinically, you are correct though. If there is no replacement and the company were smaller, the calculation would be affected materially.

The description may state that it’s a very large company, however, the calculation in their answer is still incorrect. Clearly they were not taking into consideration the fact that replacement would have an effect on the calculation when they wrote the question.

As faster typists above said, the key words in problem: “very large company” Not including the same employee will not materially change the answer. In a company with 1000 employees the answer without replacemnt is 0.0621 These questions always ahve the implicit "closest amswer’ embedded in them.

When the exact # of employees unkown, it is impossible to calculate the exact probability. Given the information in the problem, I think the approach used is very reasonable. One could even argue that replacement is being used… in which case the calculation is exactly correct. Use die instead of employees. It is possible to roll two 6’s in a row… could it be possible to pick the same employee more than once? I don’t really understand what the point of this post is. Are you trying to say this is a poorly written question? Or, is there something you don’t understand?

I was just saying it’s a poorly written question and was wondering if I should just assume that replacement doesn’t happen when it isn’t specified and the population is unknown. Clearly that’s the case.

It’s not poorly written, it’s poorly understood. The issue of replacement is negligble in a large population. If there were 10 people, you might have a point, but “very large company” is saying “assume infinite population size” is a very obvious way.

Given the information, .5x4 is the only logical way to solve it. Anything else, and you are over analyzing/wasting time on the exam.

longonCFA - .5^4… not .5*4. i was a typo in the original post as well

I’m not sure if this makes sense but I’ll go ahead anyway: My thinking was that for each employee out of the sample of 4, each employee has a 50% chance of being a male and a female. I wouldnt think that the sample of 4 is drawn one at a time. Therefore, it wouldn’t be fair to assume that when chosing the second employee, one employee should have been taken out of the population thereby decreasing the population when the 2nd employee was chosen…I’m not sure if this makes sense however. just a thought

I think we are clearly over thinking it The solution seems logic even to somebody that did not cover first book that is me

but whats more fun than overanalyzing cfa questions…especially when work is boring and you’ve got some extra time to screw around.