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: Count the number of even - numbered disks

The even - numbered disks are \(2\), \(4\), \(6\), \(8\). So, \(n(\text{even})=4\).

Step2: Count the number of even - numbered green disks

The even - numbered green disk is \(4\). So, \(n(\text{even and green}) = 1\).

Step3: Use the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the case of finite - sample spaces, \(P(\text{green}|\text{even})=\frac{n(\text{even and green})}{n(\text{even})}\).

Substitute \(n(\text{even and green}) = 1\) and \(n(\text{even})=4\) into the formula: \(P(\text{green}|\text{even})=\frac{1}{4}\)

Answer:

\(\frac{1}{4}\)