In an effort to increase the number of listeners, radio station WHACK-95.1 FM is doing sweepstakes for $50 000. The caller has to guess a four digit number to win the prize. The administration designed the sweepstakes in such a way that for every digit, any number from 0 to 9 is possible.
a) What is the probability that the first caller wins the prize if he chooses a number randomly?
b) Due to a miscommunication between administration and a technician, the sweepstakes were set up so that each digit can only occur once. What is the probability of the first caller winning the prize now?
c) The administrators did not inform the listeners well about how the digits were selected. What is the probability that the first caller wins the prize if they think that no number can be repeated in the sequence?
d) The administration intentionally misled the listeners to believe that no number can be repeated in the sequence and chose a number based on this restriction. What is the probability that the first caller wins the prize?