Question

d.)Let X be a discrete random variable equal to the number of girls you have out of 6 children.

What is P(X=2 | X=1)

P(X=2∣X=1)?

a.) Assume that a website allows only lower case letters for password required to have a length of size 5, but does not allow the following choices for the password: (1) all 5 characters are identical and (2) any sequence ending with "gk". If a 5 letter sequence is randomly selected, what is the probability that it is a valid password?

Answer #1

**(d)** P(X=2 | X=1) = P(X = 2
X = 1) / P(X = 1)

Since X =2 and X = 1 cannot occur simultaneously, hence P(X = 2 X = 1) = 0

=> P(X=2 | X=1) = 0

**(a)**

Valid passwords = Total passwords - passwords with all identical characters - password ending with "gk"

Total passwords

5 characters each with 26 possible cases =>
(26)^{5}

passwords with all identical characters

Choose any letter and make a password with all identical characters => 26

password ending with "gk"

Any character for first three positions and gk for last two positions

=> 26*26*26 = (26)^{3}

Valid passwords = (26)^{5} - 26 - (26)^{3}

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