Question

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?
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:
\[
\boxed{\frac{1}{3}}
\]