Question

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

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?

(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)

5 characters each with 26 possible cases => (26)5

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

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

=> 26*26*26 = (26)3

Valid passwords = (26)5 - 26 - (26)3

#### Earn Coins

Coins can be redeemed for fabulous gifts.