To determine the probability that Kyle picks a peanut from his handful of trail mix, let's follow these steps:
1. Identify the total number of items:
- Almonds: 2
- Peanuts: 4
- Raisins: 3
- Sunflower seeds: 5
Add all the items together to find the total number of items in the trail mix:
[tex]\[
2 + 4 + 3 + 5 = 14
\][/tex]
So, the total number of items is 14.
2. Determine the number of favorable outcomes:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Here, the favorable outcome is picking a peanut. Since there are 4 peanuts, the number of favorable outcomes is 4.
3. Calculate the probability:
The probability [tex]\( P \)[/tex] of picking a peanut is calculated as follows:
[tex]\[
P(\text{picking a peanut}) = \frac{\text{Number of peanuts}}{\text{Total number of items}} = \frac{4}{14}
\][/tex]
4. Simplify the fraction:
Simplify the fraction [tex]\(\frac{4}{14}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{4 \div 2}{14 \div 2} = \frac{2}{7}
\][/tex]
5. Conclusion:
The probability that Kyle picks a peanut from his handful of trail mix is:
[tex]\[
\frac{2}{7}
\][/tex]
Therefore, the correct answer is [tex]\(\frac{2}{7}\)[/tex].
