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.

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 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.​

GPT 3.5 · Answer

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.

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.​

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.