Question

a bag contains 3 red, 4 blue, 4 yellow, and 5 green marbles. only yellow marbles will be added to the bag. how many yellow marbles should be added to the bag to make the probability of choosing a yellow marble \\(\frac{1}{3}\\)? enter the answer in the box.

Explanation:

Step1: Define variable

Let \( x = \) yellow marbles to add.

Step2: Set up probability equation

Total marbles after adding: \( 3+4+4+5+x = 16+x \). Yellow marbles: \( 4+x \). Probability: \( \frac{4+x}{16+x} = \frac{1}{3} \).

Step3: Solve equation

Cross-multiply: \( 3(4+x) = 16+x \) → \( 12+3x =16+x \) → \( 2x=4 \) → \( x=2 \).

Answer:

2