To determine the probability that the \$10 will be in the next pocket you check after already checking two pockets, we can follow these steps:
1. Total Pockets: Initially, you have six pockets in total.
2. Checked Pockets: You have already checked two out of these six pockets and did not find the money.
3. Remaining Pockets: The number of pockets that you have not checked yet is [tex]\(6 - 2 = 4\)[/tex].
Since you have four remaining pockets and you want to find the probability that the money is in the next one you check:
4. Probability Calculation: The probability that the money is in any one of the remaining pockets is simply the ratio of the favorable outcome (finding the money in the next pocket you check) to the total possible outcomes (the total number of remaining pockets).
[tex]\[
\text{Probability} = \frac{1}{\text{number of remaining pockets}} = \frac{1}{4}
\][/tex]
So, the probability that the money is in the next pocket you check is:
[tex]\[
\boxed{\frac{1}{4}}
\][/tex]
Thus, the correct answer is:
D. [tex]\(\frac{1}{4}\)[/tex]
