Question 13

Explanation

There are $3$ boxes available. Two marbles will be placed into these boxes, with the condition that one box can only hold one marble.

Let the boxes be numbered 1, 2, 3 (from left to right).

Sample space

The total number of ways to choose 2 boxes from 3 available boxes:

Possible pairs of filled boxes:

• Boxes 2 - Adjacent
• Boxes 3 - Adjacent
• Boxes 3 - Not adjacent

Desired event

The event that marbles are not adjacent ($A$) occurs when the filled boxes are 3.

Probability

The probability that marbles are stored not adjacent to each other:

Thus, the probability that the marbles are stored not adjacent to each other is $\frac{1}{3}$.