BackRadio Station Call Letters Radio and Television station call letters must begin with either K (for stations west of the Mississippi River) or W (for stations east of the Mississippi River) and must include either two or three additional letters. How many different possibilities are there?
How many ways are there to arrange the letters in the word CALCULUS?
ZIP Code If you randomly select five digits, each between 0 and 9, with repetition allowed, what is the probability you will get the author’s ZIP code?
You want to arrange the books on your bookshelf by color. How many different ways could you arrange 12 books if 4 of them have a blue cover, 3 are yellow, and 5 are white?
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.
3. For additional security, each customer creates a 5-digit PIN (personal identification number). The table on the right shows the 10 most commonly chosen 5-digit PINs. From the table, you can see that more than a third of all 5-digit PINs could be guessed by trying these 10 numbers. To discourage customers from using predictable PINs, you consider prohibiting PINs that use the same digit more than once.
b. Would you decide to prohibit PINs that use the same digit more than once? Explain.
Board of Directors The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23
board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: University of Colorado)
37. Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Use technology to find how many ways one polluted lake and five nonpolluted lakes can be chosen.
In Exercises 49-53, use counting principles to find the probability.
53. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the
probability of choosing
b. four women?
Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.
c. If 14 subjects are randomly selected and treated at the same time, what is the probability of selecting the 14 youngest subjects?
Computer Variable Names A common computer programming rule was that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BBB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)
Social Security Numbers
A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx-xx-xxxx, where each x is a digit from 0 to 9.
b. What is the probability of correctly guessing the Social Security number of the president of the United States?
25. Playlist A band is preparing a setlist of 21 songs for a concert. How many different ways can the band play the first six songs?
Matching Probabilities In Exercises 11-16, match the event with its probability.
a. 0.95
b. 0.005
c. 0.25
d. 0
e. 0.375
f. 0.5
16. You toss a coin four times. What is the probability of tossing tails exactly half of the time?
Evaluate the given expression.
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.