. Apply the proposition involving the probability of A [ B to the union of the two events (A [ B)
and C in order to verify the result for P(A [ B [ C).
. An ATM personal identification number (PIN) consists of a four-digit sequence.
(a) How many different possible PINs are there if there are no restrictions on the possible
choice of digits?
(b) According to a representative at the authors’ local branch of Chase Bank, there are in fact
restrictions on the choice of digits. The following choices are prohibited: (1) all four digits
identical; (2) sequences of consecutive ascending or descending digits, such as 6543;
(3) any sequence starting with 19 (birth years are too easy to guess). So if one of the
PINs in (a) is randomly selected, what is the probability that it will be a legitimate PIN (i.e.,
not be one of the prohibited sequences)?
(c) Someone has stolen an ATM card and knows the first and last digits of the PIN are 8 and