In a deck of 52 playing cards, there are 12 face cards (4 Jacks, 4 Queens, 4 Kings). If you draw cards one at a time, replacing and shuffling the cards between draws, what's the probability of getting your first face card on the third draw? Choose the best answer.
○A (1 - 3/13) ^ 2 * (3/13) A.
○B. (1 - 3/52) ^ 2 * (3/52)
○C. (1 - 3/13) ^ 3 * (3/13)
D. P(X = 1) + P(X = 2) + P(X = 3)
E. P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
The correct answer is C. (1 - 3/13) ^ 2 * (3/13)
This is because there are 3 face cards in the deck of 13 remaining cards after each draw. To calculate the probability of getting your first face card on the third draw, you need to calculate the probability of not getting a face card on the first two draws (10 non-face cards out of 13 on the first draw, 9 non-face cards out of 12 on the second draw), and then getting a face card on the third draw (3 face cards out of 11).
So, the probability is (1 - 3/13) ^ 2 * (3/13) = (10/13) * (9/12) * (3/11) = 270/686 = 135/343.