3. A security keypad has 15 alpha-numeric characters on it (a) How many differen

Question

3. A security keypad has 15 alpha-numeric characters on it (a) How many different three-digit security codes are possible if the repetition of values is allowed? (b) How many different three-digit security codes are possible if the values must all be different? (c) If the three values are randomly selected (with replacement) to probability that at least one form a security code, what is the value repeats in the code? (d) A security expert believes that the three digit code allowing for repetition is not secure enough. She recommends that the code consists of k values, where k is chosen such that the probability of randomly guessing the code is less than 10-8. What is the smallest value of k for which this is true?

Explanation / Answer

a)number of codes =N(for each digit 15 choice are there) =15*15*15=3375

b)number of codes =N(for first digit 15; for second 14 and for 3rd 13 choices are there)=15*14*13= 2730

c) number of codes with repeated digits =codes with repetition -codes without repetition

=3375-2730=645

hence probability =645/3375 =0.1911

d) total k digit possible password =15k

hence probability of randomely guessing code =1/15k <10-8

taking log on both sides:

k >8/log(15)

k>6.8

k=7

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.