To determine the expected number of unsharpened colored pencils in a random selection of 50 pencils, you can use the proportion of unsharpened pencils in the entire basket.
- Total colored pencils in the basket: 300
- Unsharpened colored pencils in the basket: 3
First, find the proportion of unsharpened pencils in the basket:
\[ \text{Proportion of unsharpened pencils} = \frac{3}{300} = \frac{1}{100} \]
Next, multiply this proportion by the number of pencils Avery selects (50) to find the expected number of unsharpened pencils in that selection:
\[ \text{Expected number of unsharpened pencils} = 50 \times \frac{1}{100} = \frac{50}{100} = 0.5 \]
None of the options provided (A, B, C, D) match 0.5. It appears you may want to revisit the conditions or the answers provided. Based on the calculations, it turns out that you'd expect only 0.5 unsharpened pencils in a random selection of 50 pencils. Please double-check if there was any error in the information provided.