Statistics Problem

Question

Sixty percent of a company employees are men and 40% women. Twenty percent of the men have no college degree, 30% have a Graduate degree, and the remaining have an Undergraduate degree. Forty % of the women have an Undergraduate degree, and 40% a Graduate degree. Use the tabular approach (using a table) to find probabilities.

What is the prob of selecting at random a woman with Graduate degree?

Given that the person has a graduate degree, what is the prob that she is a woman?

What percent of all employees have no college degree?

Are gender and level of education dependent or independent events?

Which probabilities did you use in deciding if they are independent?

Answer 1

Pr(W&G) = .3(.4) = .12

W=woman, G=grad degree

Pr(W/G)Pr(G) = Pr(G/W)Pr(W)

Pr(G) = .6(.3) + .4(.4) = .18+.16 = .34

Pr(W/G) = Pr(G/W)Pr(W)/Pr(G) = .3(.4)/.34= .12/.34=about .3534

Pr(No degree) = .2(.6)+.2(.4) = .2

a degree and gender are independent

but a graduate degree and gender are dependent

and an undergraduate degree and gender are dependent

Pr(a degree/Male) = Pr(a degree/Woman) = .8

knowing the gender doesn't change the probability of having a degree. they are independent events.

But Pr(G/M)= .3 while Pr(G/W) = .4

knowing gender does make it more or less likely the person has a graduate degree

and Pr(U/M) = .5 while Pr(U/W) = .4

If it's a male it's more likely the person has an undergraduate degree

these are dependent events