Question

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

Explanation:

Step1: Count blue disks

Count the number of blue disks. There are 4 blue disks (numbered 1, 6, 2, 8).

Step2: Count even - numbered blue disks

Count the number of even - numbered blue disks. The even - numbered blue disks are 6, 2, 8, so there are 3 even - numbered blue disks.

Step3: Calculate probability

The probability formula for conditional probability (in this case, given a blue disk is selected) is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (even - numbered blue disks) is 3 and the total number of outcomes (blue disks) is 4. So the probability \(P = \frac{3}{4}\).

Answer:

\(\frac{3}{4}\)