A government agency has 6000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by sex.

a.      Calculate the overinvolment ratio (use 1 digit after decimal point) to measure effect of being female on preferring Flexible hours. 

b.      What is the probability of selecting an male employee, given that the person is prefered flexible hours?(use 3 digits after decimal point) 

c.      If we randomly select 4 employees (with replacement) who preferred Flexible hours, what is the probability that none of them are Female?(use 5 digits after decimal point) 

d.      If we randomly select 2 employees (without replacement) who preferred Flexible hours, what is the probability that none of them are Female?(use 3 digits after decimal point) 

The following table shows the number of students in three different degree programs and whether they are graduate or undergraduate students:

a.      Calculate the overinvolment ratio (use 2 digits after decimal point) to measure effect of being undergraduate student on majoring in Engineering. 

b.      What is the probability of selecting a graduate student, given that this student is studing engineering?(use 2 digits after decimal point) 

c.      If we randomly select 4 students (with replacement) who are studing engineering, what is the probability that none of them are undergraduate?(use 5 digits after decimal point) 

d.      If we randomly select 2 students (without replacement) who are studing engineering, what is the probability that none of them are undergraduate?(use 4 digits after decimal point) 

A garage door opener has six toggle switches, each with three settings: up, center and down. How many settings are possible in which two switches are up, two are down, and two are in the center?

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female. The number of sample points in this experiment is:

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is:

Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∩ B) =

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A | B) =

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =