Question

Exercise 48. Suppose that a computer randomly generates four-digit codes to match ATM pin codes among {0000, 0001, . . . , 9999}.

1. Explain carefully why there are 10000 possible four-digit codes when the digits are among 0-9.

2. Note that 10000 = 104. Explain how this connects the number of digits, the choice of digits, and the possible four-digit pin codes.

3. Among the 10000 possible four-digit pin codes, how many involve exactly three 1s or exactly three 2s? Write out the possibilities.

4. Using the previous part, what is the probability that a randomly selected four-digit pin code will contain exactly three 1s or exactly three 2s?

5. Using the complement rule, what is the probability that a randomly selected four-digit pin code will not contain exactly three 1s or exactly three 2s?

Answer 1