Question

you have a 3-card deck containing a king, a queen, and a jack. you draw a random card, then put it backand draw a second random card. calculate the probability that you draw exactly i king

Answer 1

our first set of branches has 3 branches with prob 1/3: J, Q, and K. From each of these there are 2 branches containing the 2 cards you didnt select in your first draw each with prob 1/2. Ways to get 1 Jack:
J-Q,J-K,Q-J,K-J
each of these has prob (1/3)*(1/2)=1/6 so we have 4*(1/6)=4/6

P(1 Jack)=2/3

Answer 2

or

You want face card on draw one and non-face on draw two...or vice versa.

Probability is the same regardless of which order so we find one and then double it.

Probablity of face then non-face would be 3/5 x 2/5 (since there's replacement).
Which is 6/25...

Double this for the other possibility (non-face followed by face)

Answer 3

I'm all screwed up today.

Since it's asking that, the answer should be 1 in 9 since you have a 1 in 3 chance of picking a king each time (1/3 * 1/3).