How many cards must be chosen from a deck to guarantee that atleast i. two…

Solution:

• i. Two aces of two kinds (at least two aces): Worst-case you could draw all 48 non-ace cards first. The next two draws could be the first two aces, so you need 48 + 2 = 50 cards to guarantee at least two aces.

• ii. Two aces are chosen: Same reasoning as (i): to force two aces in the worst case you must allow for drawing all 48 non-aces first, so 50 cards are required.

• iii. Two cards of the same kind (same rank): There are 13 ranks. You could pick one card from each rank (13 cards) without getting a pair; the next card (14th) must match one of the ranks. Thus 14 cards guarantee a pair.

• iv. Two cards of two different kinds (two different ranks): In the worst case you might draw all four cards of a single rank (4 cards); the next card (5th) must be of a different rank. Therefore 5 cards guarantee two different ranks.

Final answers: 50, 50, 14, 5