To determine the probability that the \$10 will be in the next pocket you check, let’s follow these steps:
1. Total Number of Pockets:
Initially, you have 6 pockets in your cargo pants.
2. Pockets Already Checked:
You have checked 2 pockets so far, and the money was not found in either of them.
3. Remaining Pockets to Check:
Since you have already checked 2 out of the 6 pockets, you have [tex]\(6 - 2 = 4\)[/tex] pockets left to check.
4. Probability Calculation:
The probability that the money is in any one of the remaining pockets is equal, as there is no reason to believe any pocket is more likely to contain the money than any other. Therefore, the probability that the money is in any one specific remaining pocket (including the next one you check) is:
[tex]\[
\frac{1}{\text{number of remaining pockets}} = \frac{1}{4}
\][/tex]
Thus, the probability that the money will be in the next pocket you check is [tex]\( \frac{1}{4} \)[/tex].
Therefore, the correct answer is D. [tex]\( \frac{1}{4} \)[/tex].
