To determine the probability that Mr. Sabol will choose a pencil first and then a pen without replacement from his collection of 12 pens and 18 pencils, we need to follow these steps:
1. Calculate the total number of writing implements:
- Pens: 12
- Pencils: 18
- Total items = Pens + Pencils = 12 + 18 = 30
2. Determine the probability of choosing a pencil first:
- The probability of choosing a pencil first is the number of pencils divided by the total number of items.
[tex]\[
\text{Probability of choosing a pencil first} = \frac{\text{Number of pencils}}{\text{Total number of items}} = \frac{18}{30} = 0.6
\][/tex]
3. Determine the probability of choosing a pen second after a pencil has been chosen:
- After choosing a pencil, one item is removed, so the total number of items left is 29.
- The number of pens remains 12.
- The probability of choosing a pen after a pencil has been chosen is the number of pens divided by the remaining total number of items.
[tex]\[
\text{Probability of choosing a pen second} = \frac{\text{Number of pens}}{\text{Remaining total number of items}} = \frac{12}{29} \approx 0.41379310344827586
\][/tex]
4. Calculate the combined probability:
- The combined probability is the product of the individual probabilities.
[tex]\[
\text{Combined probability} = \left(\frac{18}{30}\right) \times \left(\frac{12}{29}\right) = 0.6 \times 0.41379310344827586 \approx 0.2482758620689655
\][/tex]
5. Convert the combined probability to a fraction and simplify:
- Converting the combined probability to a fraction and simplifying it gives:
[tex]\[
0.2482758620689655 = \frac{36}{145}
\][/tex]
Thus, the probability that Mr. Sabol will choose a pencil first and then a pen is \(\frac{36}{145}\).
Answer:
[tex]\[
\boxed{B. \frac{36}{145}}
\][/tex]
