Question

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. 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.

Explanation:

Step1: Calculate total initial cards

Initial cards: red (2) + yellow (2) + black (4) = $2 + 2 + 4 = 8$ cards.

Step2: Let $x$ be yellow cards to add

After adding $x$ yellow cards, yellow cards = $2 + x$, total cards = $8 + x$.
We want $\frac{2 + x}{8 + x} = 0.5$ (50% chance).

Step3: Solve the equation

Multiply both sides by $8 + x$: $2 + x = 0.5(8 + x)$
Expand: $2 + x = 4 + 0.5x$
Subtract $0.5x$: $2 + 0.5x = 4$
Subtract 2: $0.5x = 2$
Multiply by 2: $x = 4$

Answer:

4