REAL STATISTICS REAL DECISIONS Putting it all together 186 CHAPTER 3 Probability 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 1 608 , 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. EXERCISES 1. How Would You Do It? (a) How would you investigate the question of what password requirements you should set to meet the security guidelines? (b) What statistical methods taught in this chapter would you use? 2. Answering the Question (a) What password requirements would you set? What characters would be allowed? (b) Show that the probability that a password is guessed on one try is less than 1 608 , when the requirements in part (a) are used and all passwords are equally likely. 3. Additional Security 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. (a) How would this requirement affect the number of possible 5-digit PINs? (b) Would you decide to prohibit PINs that use the same digit more than once? Explain. Most Popular 5-Digit PINs Rank PIN Percent 1 12345 22.80% 2 11111 4.48% 3 55555 1.77% 4 00000 1.26% 5 54321 1.20% 6 13579 1.11% 7 77777 0.62% 8 22222 0.45% 9 12321 0.41% 10 99999 0.40% (Source: Datagenetics.com)
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