Given that the numbered disks are placed in a box, you need to find the probability of selecting an odd number, given that a green disk is selected.
Therefore, you need to use the Conditional Probability Formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, let be "A" the event of selecting an odd number, and "B" the event of selecting a green disk.
You can identify that:
- There are a total of 8 disks.
- There are 4 green disks that have odd numbers.
- There are a total of 7 green disks.
Therefore, you can determine that:
[tex]P(A\cap B)=\frac{4}{8}=\frac{1}{2}[/tex]And:
[tex]P(B)=\frac{7}{8}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]P(A|B)=\frac{\frac{1}{2}}{\frac{7}{8}}=\frac{1\cdot8}{2\cdot7}=\frac{8}{14}=\frac{4}{7}[/tex]Hence, the answer is:
[tex]\frac{4}{7}[/tex]