Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.
Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
I get C.
lets first find the probability of no pairs then we will subtract it from 1.
1st card . He can pick any so probability 1
second card. he has 11 and he can pick any 10 of them apart from the one which is similar to the previous one already picked so probability is 10/11
third card. He can pick 8 of the 10 remaining. leaving the 2 already picked.so probability 8/10
fourth card. similar as above it will be 6/9
so total probability of no pairs is
10/11 * 8/10 * 6/9 = 16/33. there to get atleast one matching pair, probability is 1- 16/33 = 17/33