4. Probability

Evaluate the given expression. $_9P_4$

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be

interviewed about the work environment.

Find the probability of choosing four third-shift workers.

Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team.

b. What is the probability that none of the offices are filled by members of the debate team?

In Exercises 41-44, perform the indicated calculation.

44. (5C3)/(10C3)

In Exercises 7-14, perform the indicated calculation.

12. (10C7)/(14C7)

2. How many possible variations are there in Mozart's Musical Dice Game minuet? Explain.

You work in the security department of a bank’s website. To access their accounts, customers of the bank must create an 8-digit password. It is your job to determine the password requirements for these accounts. Security guidelines state that for the website to be secure, the probability that an 8-digit password is guessed on one try must be less than 1/60^8, assuming all passwords are equally likely.

Your job is to use the probability techniques you have learned in this chapter to decide what requirements a customer must meet when choosing a password, including what sets of characters are allowed, so that the website is secure according to the security guidelines.

2. Answering the Question

a. What password requirements would you set? What characters would be allowed?

23. Footrace There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third?

Teed Off When four golfers are about to begin a game, they often toss a tee to randomly select the order in which they tee off. What is the probability that they tee off in alphabetical order by last name?

[NW] Selecting a Jury

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.

b. What is the probability of selecting a jury of all faculty?

Quinela In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 144th running of the Kentucky Derby had a field of 20 horses. What is the probability of winning a quinela bet if you randomly select the horses?

Mendel’s Peas Mendel conducted some of his famous experiments with peas that were either smooth yellow plants or wrinkly green plants. If four peas are randomly selected from a batch consisting of four smooth yellow plants and four wrinkly green plants, find the probability that the four selected peas are of the same type.