Question

There are 3 balls in a hat; one with the number 3 on it, one with the number 4 on it, and one with the number 9 on it. You pick a ball from the hat at random and then you flip a coin. Using a tree diagram , obtain the sample space for the experiment. List the elements that make up the sample space.

3 4 9 H, 3 4 9 T

3 H T, 4 H T, 9 H T

3 H, 4 H, 9 H

3 H, 3 T, 4 H, 4 T, 9 H, 9 T

Answer 1

The elements of the sample space are as follows:

3 H

3 T

4 H

4 T

9 H

9 T

How to solve

The sample space for the experiment, considering picking a ball and then flipping a coin, would be best represented by a tree diagram.

Using the provided information:

Three balls with numbers: 3, 4, and 9.

The coin has two sides: Heads (H) and Tails (T).

Pick a ball

/ \ \

3 4 9

/ \ / \ / \

H T H T H T

Each outcome represents a possible result when first selecting one of the numbered balls and then flipping the coin, resulting in a combination of number and coin flip.