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);
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).
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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