Question

(3) If you are drawing 3 cards (one-by-one without replacement) from a shuffled deck of S2 cards, what is the total count of the sample space S this time? If A={all 3 are red}, B= {all 3 are diamonds), C = {all 3 are the king of spades), D = {all 3 are of the same color}, E= {all 3 are from the same suit}, F= {all 3 of them are the same card}, find P(A), P(B), P(C), P(D), P(C), and P(F) in this case. [1+1+1+1+1+1+1]

Answer 1

Total sample sample space = 52C3 = 52! / (3! * (52 - 3)!) = 22100

P(A) = 26C3 / 52C3 = 2600 / 22100 = 2/17

P(B) = 13C3 / 52C3 = 286 / 22100 = 11/850

P(C) = 0, because there is only one king of spade

P(D) = P(all 3 are red) + P(all 3 are black) = (26C3 / 52C3) + (26C3 / 52C3) = (2600 / 22100) + (2600 / 22100) = 4/17

P(E) = 4C1 * 13C3 / 52C3 = 4 * 286 / 22100 = 22/425

P(F) = 0