Most bank cards can be used to access an account by entering a 4-digit personal identification number (PIN). However, knowing these four digits is not enough to access the account. The digits have to be in the correct order.
Consider Lee’s account, where four digits used in opening it are , _, _) , and . Lee can’t remember the numbers, but he does know that none of the four numbers are the same. He is sure that none of the four numbers repeat.
Lee might have to start randomly guessing since he really needs some money fast.
1. How many 4-digit pin numbers are possible for Lee’s account? Explain your reasoning.
2. If Lee randomly guesses one of the possible numbers, what is the probability that he would type in the correct PIN the first time?
The bank card will be canceled after two failed attempts at entering the PIN.
3. If he randomly guesses a second number, what is the probability he will be able to use his bank card before it is canceled?