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.