Please give me some hints on the following Statistics problem.?

Question

A company has five applicants for two positions: two women and three men. Supoose that the five applicants are equally qualifies and that no preference is given for choosing either gender. Let x equal to the number of women chosen to fill the two positions.
(a) Write the formula for p(x), the probability distribution of x.
(b) What are the mean and variance of this distribution?
(c) Contruct a probability histogram for x.

Answer 1

This involve nCr (aka 'n choose r'), ie. n! / [r! (n - r)!], where '!' denotes the factorial (you'll find this on your calculator, hopefully). In considering (a), we first need to work out how many ways there are of choosing two people from the five applicants. For this, just apply the given forumula with n=5 and r=2:

5! / 2!3! = 5*4 / 2 = 10.

Now, for x=2, we need only observe that there is only one way of choosing both women. Hence p(2) = 1/10.

For x=0, we need to work out how many ways there are of choosing two men from the three male applicants. Again, apply the formula (for n=3, r=2):

3! / 2!1! = 3.

Hence p(0) = 3/10.

For x=1, well, we know appointing two women or none counts for 4 of the 10 possible outcomes; therefore there must be 10 - 4 = 6 ways of appointing only one woman. Hence p(1) = 4/10 = 2/5.

Answering (b) is now just a matter of applying the definitions of mean and variance you should've been given in class. Eg

the mean of x = 0*p(0) + 1*p(1) + 2*p(2) etc.

And answering (c) merely involves drawing a bar graph of your probability distribution function, plotting p(x) against x. I can hardly do that for you with a keyboard! The link below should give you an idea of what one should look like.

Answer 2

Why? that's all bs. No real world application. Even if gender bias and exactly equal qualifications are possible, which they are not, the women simply have a 2 out of five chance of getting one of the jobs. in reality, they either have no chance or all the chances. if the gender bias kicks in. Maybe the company will hire the women because they need to make their quota of female employees. Maybe they get hired because they look good, or not be cause they don't. Why do a bs problem that has no bearing on real world goings on? That's what i have always hated about that kind of math, no real purpose to it. forget it and solve a real problem.