Question

The numbered disks shown are placed in a boxand one disk is selected at random. Find theprobability of selecting an odd number, given that agreen disk is selected.Find the probability of selecting an odd number, given that a green disk is selected.(Type an integer or a simplified fraction.)

Answer 1

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:

`P(A|B)=(P(A\cap B))/(P(B))`

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:

`P(A\cap B)=(4)/(8)=(1)/(2)`

And:

`P(B)=(7)/(8)`

Then, you can substitute values into the formula and evaluate:

`P(A|B)=((1)/(2))/((7)/(8))=(1\cdot8)/(2\cdot7)=(8)/(14)=(4)/(7)`

Hence, the answer is:

`(4)/(7)`