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 arc equally likely. How many outcomes in sample space S? How many outcomes in event A? How many outcomes in event B? How many outcomes in event A 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

here as total number of charecters =26+26+10 =62

1) as there are 52 possible charecters for 6 places . hence total number of passwords in sample space =626

2)as event A will count only letters hence total outcomes in A = 526

3) similarly total outcomes in B =106

4)as A and B are disjoint , means share nothing in common hence AnB =0

5) P(A) =(52/62)6

6)P(A|B) =P(AnB)/P(B) =0 ; as P(AnB) =0

7) no they are not independent. for independence P(A|B) =P(A) which is not the case.

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