Question

Patricia was having fun playing a card game. To win the game, she needed the next two cards dealt to be yellow cards. There are 12 cards left in the deck, and three are yellow. What is the probability that the two cards dealt to Patricia will both be yellow?

A) 1/4
B) 1/22
C) 3/44
D) 1/24

Answer 1

The probability of Patricia drawing two yellow cards sequentially without replacement from a deck of 12 cards with 3 yellow is 1/22.

Step-by-step explanation:

The probability that the two cards dealt to Patricia will both be yellow can be calculated by multiplying the probability of drawing one yellow card and then another without replacement. With 12 cards total and 3 yellow, the probability of drawing a yellow card first is 3/12 or 1/4. If Patricia draws one yellow card, there will be 11 cards left and 2 of them will be yellow. The probability for the second card being yellow is then 2/11. Multiplying these probabilities gives 1/4 × 2/11 = 2/44 or 1/22, which is option B.