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04:39Your dorm enters 15 out of 65 plastic numbered ducks in a duck race. The ducks are all dumped into a stream and drift to the finish line. What is the probability that three of your dorm's ducks finish first, second, and third?
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).
A person's building access code is their first and last initials and four digits.
You know a person's first name only, and you know that the last digit is odd. What is the probability of guessing this person's code on the first try?
7. There are 16 students giving final presentations in your history course.
b. Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on
the same unit are indistinguishable from each other?
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.
4. The table on the left shows the secondary school student enrollment levels (in thousands by grade) in Oklahoma and Texas schools in a recent year. (Source: U.S. Nation
for Education Statistics)
A student in one of the indicated grades and states is randomly selected. Find the probability of selecting a student who
a. is in ninth grade.
