Q1) A computer system uses passwords that are five characters, and each character is one of of the 26 letters (a-z) or 10 integers (0-9). The first character has to be a letter. You may assume that passwords are not case sensitive. Determine: (a) the total number of possible passwords (b) the proportion of passwords that begin with a consonant; (c) the proportion of passwords that end with an even number (0,2,4,6,8);

Q1) A computer system uses passwords that are five characters, and each character is one of

of the 26 letters (a-z) or 10 integers (0-9). The first character has to be a letter.

You may assume that passwords are not case sensitive.

Determine:
(a) the total number of possible passwords

(b) the proportion of passwords that begin with a consonant;
(c) the proportion of passwords that end with an even number (0,2,4,6,8);

(d) the proportion of possible passwords begin with a consonant OR end with an even number (OR both)

hint: use the addition law of probability: P(A U B) = P(A) + P(B) - P(A ∩ B)
(e) if a password was selected at random, what is the probability the password would read the

same backwards as forwards?

(f) solve (e) by making a simulation in R i.e. write some code to generate lots of passwords using the sample function, and count how many time you get a palindromic password. You will want to get a large number of samples here for to generate an accurate estimate (i.e. 100,000).