A random digit generator on an electronic calculator is activated twice to simulate a random two-digit number. Theoretically, each digit from 0 to 9 is just as likely to appear on a given trial as any other digit.
(a) How many random two-digit numbers are possible?
(b) How many of these numbers begin with the digit 2?
(c) How many of these numbers end with the digit 9?
(d) How many of these numbers begin with the digit 2 and end with the digit 9?
(e) What is the probability that a randomly formed number ends with 9 given that it begins with a 2. Did you anticipate this result?