A bag with 6 marbles has 2 blue marbles, 1 yellow marble, and 3 red marbles. A marble is chosen from the bag at random. What is the probability that it is blue?

Question

Write your answer as a fraction in simplest form.

Answer 1

To find the probability of drawing a blue marble from the bag, we first need to determine the total number of marbles and the number of favorable outcomes.

The bag contains:

• 2 blue marbles
• 1 yellow marble
• 3 red marbles

Now, we can calculate the total number of marbles: \[ \text{Total marbles} = 2 \text{ (blue)} + 1 \text{ (yellow)} + 3 \text{ (red)} = 6 \text{ marbles} \]

The number of favorable outcomes (getting a blue marble) is: \[ \text{Favorable outcomes} = 2 \text{ (blue marbles)} \]

The probability \( P \) of drawing a blue marble is given by the formula: \[ P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{2}{6} \]

Next, we simplify the fraction \( \frac{2}{6} \): \[ \frac{2}{6} = \frac{1}{3} \]

Thus, the probability that a marble chosen at random from the bag is blue is: \[ \boxed{\frac{1}{3}} \]