Question

A box contains 20 marbles. There are equal amounts of blue, green, red, and yellow ones. If one of the marbles is picked out at random, what is the probability that it will be yellow?

Answer 1

To find the probability of picking a yellow marble from the box, we first need to determine how many marbles of each color are in the box.

Since there are 20 marbles in total and the marbles are distributed equally among four colors (blue, green, red, and yellow), we can calculate the number of marbles of each color as follows:

\[
\text{Number of marbles of each color} = \frac{\text{Total number of marbles}}{\text{Number of colors}} = \frac{20}{4} = 5
\]

Thus, there are 5 yellow marbles in the box.

The probability \( P \) of picking a yellow marble is given by the formula:

\[
P(\text{yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{5}{20}
\]

Now, we can simplify the fraction:

\[
P(\text{yellow}) = \frac{5}{20} = \frac{1}{4}
\]

Therefore, the probability that a randomly picked marble will be yellow is \( \frac{1}{4} \).