Question

I've done A to E but I'm stuck in F. A computer has been programmed to...

I've done A to E but I'm stuck in F.

A computer has been programmed to generate, uniformly at random, an eight-character password, with each character being either one of 26 lower-case letters (a-z), one of 26 upper-case letters (A-Z) or one of 10 integers (0-9).

a) Let Ω be the set of all possible passwords generated by this computer. What is the size |Ω| of this sample space? Determine the probability that a randomly generated password

b) contains only letters.

c) contains only numbers.

d) contains at least 1 number.

e) contains exactly 2 numbers.

A website requires registration using an eight-character password containing at least one lower-case letter, at least one upper-case letter and at least one number.

f) What is the probability that a randomly generated password satisfies these requirements?

Math   Statistics-And-Probability   
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