Question

A bag contains 4 red pencils, 6 blue pencils, and 5 green pencils. A pencil is randomly selected, its color is recorded, and it is returned to the bag. This is repeated 1350 times.

How many times is it expected that a green pencil will be selected?

Responses

approximately 360 times
approximately 360 times

approximately 450 times
approximately 450 times

approximately 540 times
approximately 540 times

approximately 900 times

Answer 1

To find the expected number of times a green pencil will be selected, we first need to determine the total number of pencils in the bag.

The bag contains:
- 4 red pencils
- 6 blue pencils
- 5 green pencils

Total number of pencils = 4 + 6 + 5 = 15 pencils.

Next, we calculate the probability of selecting a green pencil:

\[
P(\text{green}) = \frac{\text{number of green pencils}}{\text{total number of pencils}} = \frac{5}{15} = \frac{1}{3}.
\]

Now, we need to find the expected number of times a green pencil will be selected in 1350 trials. The expected number can be calculated using:

\[
\text{Expected number of green pencils} = P(\text{green}) \times \text{total number of selections}.
\]

So, we have:

\[
\text{Expected number of green pencils} = \frac{1}{3} \times 1350 = 450.
\]

Thus, the expected number of times a green pencil will be selected is approximately **450 times**.