Let's break down the problem into smaller parts and calculate the required probabilities step-by-step.
1. Total Number of Pens:
Jeff has 4 red pens and 2 blue pens.
[tex]\[
\text{Total number of pens} = 4 + 2 = 6
\][/tex]
2. Total Number of Highlighters:
Jeff has 1 yellow highlighter and 4 green highlighters.
[tex]\[
\text{Total number of highlighters} = 1 + 4 = 5
\][/tex]
3. Probability of Drawing a Blue Pen:
The probability of drawing a blue pen is the ratio of the number of blue pens to the total number of pens.
[tex]\[
\text{Probability of drawing a blue pen} = \frac{\text{Number of blue pens}}{\text{Total number of pens}} = \frac{2}{6} = \frac{1}{3}
\][/tex]
4. Probability of Drawing a Yellow Highlighter:
The probability of drawing a yellow highlighter is the ratio of the number of yellow highlighters to the total number of highlighters.
[tex]\[
\text{Probability of drawing a yellow highlighter} = \frac{\text{Number of yellow highlighters}}{\text{Total number of highlighters}} = \frac{1}{5}
\][/tex]
5. Joint Probability:
The events of drawing a pen and a highlighter are independent of each other. Therefore, the joint probability of both events occurring is given by the product of their individual probabilities.
[tex]\[
\text{Probability of drawing a blue pen and a yellow highlighter} = \left(\frac{1}{3}\right) \times \left(\frac{1}{5}\right) = \frac{1}{15}
\][/tex]
Thus, the probability that Jeff will grab a blue pen and a yellow highlighter is:
[tex]\[
\boxed{\frac{1}{15}}
\][/tex]
