Question

You have a 3-card deck containing a king, a queen, and a jack. You draw a random card, then without putting it back you draw a random second card from the ones that are left. Use a tree diagram to calculate the probability that you draw exactly 1 jack.

A.
B.
C.
D.
E.

Answer 1

your 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

where do you get 4 from