Select the correct answer.

You are wearing a pair of cargo pants with six pockets. You've put \[tex]$10 in one of the pockets, but you cannot remember which one. After checking two pockets without success, what is the probability that the money will be in the next pocket you check?

A. $[/tex]\frac{1}{8}[tex]$
B. $[/tex]\frac{1}{6}[tex]$
C. $[/tex]\frac{3}{5}[tex]$
D. $[/tex]\frac{1}{4}$



Answer :

Let's work through this problem step by step.

1. Total Pockets:
You have 6 pockets in total.

2. Pockets Already Checked:
You have checked 2 pockets already, and you did not find the money in either of them.

3. Remaining Pockets:
Since you have checked 2 pockets out of 6, there are [tex]\( 6 - 2 = 4 \)[/tex] pockets left.

4. Probability:
The probability of finding the money in the next pocket you check is determined by the number of remaining pockets. Since there are 4 pockets left and only one of these pockets contains the money, the probability of the money being in the next pocket you check is [tex]\(\frac{1}{4}\)[/tex].

Therefore, the correct answer is:
D. [tex]\(\frac{1}{4}\)[/tex]