A computer system uses passwords that contain exactly six characters, and each c

Question

A computer system uses passwords that contain exactly six characters, and each character is one of the 26 lowercase letters (a-z) or 26 uppercase letters (A-Z) or 10 integers (0-9). Let S denote the set of all possible password, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords in S are equally likely. How many outcomes in sample space 5? How many outcomes in event A? How many outcomes in event B? How many outcomes in event A intersection B? P(A) = P(A|B) = Are events A and B independent? Why? Bonus! P(password contains exactly 2 integers given that it contains at. least 1 integer)

Explanation / Answer

A)S can have any of the possible passwords

Number of possible letters or integers->26+26+10=62

Number of possible outcomes->62^6=56800235584

B)outcomes in A->52^6=19770609664

C) outcomes in B->10^6=1000000

D)common elements in A and B=0

E)P(A)=19770609664/56800235584=0.3481

F)P(A|B)=0

G)A and B are not independent as A and B are mutually exclusive.

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