Question

Which is more likely: event A, drawing an ace, then a king, then a queen, or event B, drawing three consecutive aces? Assume that cards drawn are not returned to the pack. How does your answer change if cards are returned after each draw? Explain how you determined your answers.

Answer 1

if cards are not put back in the pack then:
4/54 * 4/53 * 4/52 = 2/27 * 4/53 * 1/13 (ace+king+queen)
4/54 * 3/53 * 2/52 = 2/27 * 3/53 * 1/13 *1/2 (ace*3)
if we compare the two and simplify we get to
4 > 3/2
so chnc(ace+king+queen)>chnc(ace*30)
if cards are put back in the pack then
4/54*4/54*4/54=4/54*4/54*4/54 so they have a equal chance of happening