Certainly! Let's break it down step-by-step:
1. Understand the Problem:
We need to determine the probability of picking a green or purple pencil from the box. We are given the probabilities of picking a green pencil and a black pencil.
2. Given Data:
- Probability of picking a green pencil, [tex]\( P(\text{green}) = 41.2\% \)[/tex]
- Probability of picking a black pencil, [tex]\( P(\text{black}) = 12.7\% \)[/tex]
3. Concept to Use:
The probability of picking either a green or purple pencil is the complement of the probability of picking a black pencil. This is because the pencils can only be green, black, or purple; thus, the probabilities for these three outcomes must sum up to 100%.
4. Calculation:
- Probability of picking a black pencil, [tex]\( P(\text{black}) = 12.7\% \)[/tex]
- Therefore, the probability of not picking a black pencil (i.e., picking either a green or purple pencil) is [tex]\( 100\% - P(\text{black}) \)[/tex].
5. Perform Calculation:
[tex]\[
P(\text{green or purple}) = 100\% - 12.7\% = 87.3\%
\][/tex]
6. Result:
The probability of picking either a green or purple pencil from the box is [tex]\( \boxed{87.3\%} \)[/tex].
