Question

the numbered disks shown are placed in a box and one disk is selected at random. find the probability of selecting a green disk, given that an even number is selected. what is the probability of selecting a green disk, given that an even number is selected? (type an integer or a simplified fraction.)

Explanation:

Step1: Identify even - numbered disks

The even - numbered disks are 2, 4, 6, 8. So there are 4 even - numbered disks.

Step2: Identify green and even - numbered disks

The green and even - numbered disks are 4. So there is 1 green and even - numbered disk.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of equally - likely outcomes, if $A$ is the event of selecting a green disk and $B$ is the event of selecting an even - numbered disk, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in $A\cap B$ and $n(B)$ is the number of elements in $B$. Here, $n(A\cap B) = 1$ and $n(B)=4$. So the probability is $\frac{1}{4}$.

Answer:

$\frac{1}{4}$