Question

Suppose that a five-letter password can consist of uppercase and lowercase letters. If such a password is generated at random, what is the probability it will consist of only uppercase letters?

Answer 1

Uppercase Letters : (A-Z) : Total of 26

Lowercase Letters : (a-z) : Total of 26

So, the 5-letter password can contain any of these 52 characters

Probability that it will consist only uppercase letters is required-

Total possibilities (assuming repetitions are allowed) = (52)^5

Combinations with only uppercase letters = (26)^5

So, required probability = (26)^5/(52)^5

= (1/2)^5 = 1/32

Probability that the password will contain only uppercase letters is 1/32

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