BackIn Exercises 45-48, use combinations and permutations.
46. Five players on a basketball team must each choose one of the five players on the opposing team to defend. In how many ways can the players choose their defensive assignments?
In Exercises 45-48, use combinations and permutations.
48. An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the two people?
In Exercises 49-53, use counting principles to find the probability.
50. A security code consists of three letters and one digit. The first letter cannot be A, B, or C. What is the probability of guessing the security code on the first try?
In Exercises 49-53, use counting principles to find the probability.
52. A class of 40 students takes a statistics exam. The results are shown in the table at the left. Three students are selected at random. What is the probability that
b. all three students received a C or better?
In Exercises 49-53, use counting principles to find the probability.
52. A class of 40 students takes a statistics exam. The results are shown in the table at the left. Three students are selected at random. What is the probability that
d. all three students received a B or a C?
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
c. two men and two women?
In Exercises 49-53, use counting principles to find the probability.
51. A shipment of 200 calculators contains 3 defective units. What is the probability that a sample of three calculators will have
c. at least one defective calculator?
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?
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?
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.
2. How many possible variations are there in Mozart's Musical Dice Game minuet? Explain.
5. Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total.
a. What is the theoretical probability of each total from 1 to 11?
b. Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a).
Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.
62. Find the probability of being dealt three of a kind (the other two cards are different from each other).
In Exercises 41-44, perform the indicated calculation.
42. 8P6
In Exercises 41-44, perform the indicated calculation.
44. (5C3)/(10C3)