In a game, a player randomly pulls a card from a stack that contains 2 red, 2 yellow, and 4 black cards. Only yellow cards will be added to the stack. How many yellow cards should be added to the stack to make the chance of pulling a yellow card 50%? Enter the answer in the box.
To find the number of yellow cards needed to make the chance of pulling a yellow card 50%, we need to set up an equation.
Let x represent the number of yellow cards added to the stack.
The total number of cards in the stack after adding x yellow cards would be (2 + 2 + 4 + x).
The probability of pulling a yellow card from the stack is given by the number of yellow cards (2 + x) divided by the total number of cards (2 + 2 + 4 + x), which can also be written as:
(2 + x) / (2 + 2 + 4 + x) = 0.5
To solve this equation, we can cross-multiply and simplify:
(2 + x) = 0.5 * (2 + 2 + 4 + x)
2 + x = 0.5 * (8 + x)
2 + x = 4 + 0.5x
0.5x - x = 4 - 2
(0.5 - 1)x = 2
-0.5x = 2
x = 2 / -0.5
x = -4
Since we can't have a negative number of yellow cards added to the stack, the answer is 0.