Certainly! Let's go through the problem step-by-step to find the probability that a randomly picked candy is not yellow.
1. Determine the total number of candies in the bag:
- Red candies: 42
- Green candies: 45
- Yellow candies: 20
- Purple candies: 32
Adding these together gives us the total number of candies in the bag:
[tex]\[
\text{Total candies} = 42 + 45 + 20 + 32
\][/tex]
[tex]\[
\text{Total candies} = 139
\][/tex]
2. Calculate the number of candies that are not yellow:
To find the number of candies that are not yellow, we subtract the number of yellow candies from the total number of candies:
[tex]\[
\text{Not yellow candies} = \text{Total candies} - \text{Yellow candies}
\][/tex]
[tex]\[
\text{Not yellow candies} = 139 - 20
\][/tex]
[tex]\[
\text{Not yellow candies} = 119
\][/tex]
3. Find the probability of picking a candy that is not yellow:
The probability of an event is given by the ratio of the favorable outcomes to the total outcomes. In this case, the favorable outcomes are picking a candy that is not yellow, and the total outcomes are the total number of candies.
[tex]\[
P(\text{not yellow}) = \frac{\text{Number of not yellow candies}}{\text{Total number of candies}}
\][/tex]
[tex]\[
P(\text{not yellow}) = \frac{119}{139}
\][/tex]
4. Simplify the probability:
The fraction [tex]\(\frac{119}{139}\)[/tex] is already in its simplest form. So, we can leave it as it is or convert it to a decimal form if desired.
[tex]\[
P(\text{not yellow}) \approx 0.8561
\][/tex]
Therefore, the probability that a randomly picked candy is not yellow is [tex]\( \boxed{0.8561} \)[/tex].
