In a stack of cards, 8 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 1/2. What is the number of cards in the stack?  Choose the correct choice from the following options:
A) 10 B) 11 C) 12 D) 15 E) 18
This question can be solved by TESTing THE ANSWERS.   We're told that we have 9 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 1/2. We're asked for the TOTAL number of cards.   Normally, when TESTing THE ANSWERS, we should start with either B or D. Answer B looks easier, so let's start there.   Answer B: 11 total cards   With 11 total cards, and 8 blue cards, the probability of pulling two blue cards is...   (8/11)(7/10) = 56/110~0.509   Since 1/2= 
<gadget id="calculator">1/2</gadget>
<output>1/2 = around 0.5</output>
0.5, this is clearly the answer.   11
<result>B</result>
In a stack of cards, 8 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 1/2. What is the number of cards in the stack?