Question

A bag contains 1 red tile, 1 blue tile, 1 green tile, 1 yellow tile, and 1 purple tile. Kaison chooses a tile from the bag, records its color, and then replaces the tile. She repeats this procedure a total of 50 times. Her results are shown in the table.

How does the experimental probability of choosing a yellow tile compare with the theoretical probability of choosing a yellow tile?
The experimental probability is the same as the theoretical probability.
The experimental probability is twice the theoretical probability.
The experimental probability is one-half of the theoretical probability.
The experimental probability is one-fifth of the theoretical probability.

Answer 1

Correct option is 1st option

Explanation:

1. The theoretical probability is a ratio of the number of favorable outcomes to the number of possible outcomes,

`Pr_(theoretical)=\frac{\text{number of all favorable outcomes}}{\text{numberof all possible outcomes}}.`

2. The experimental probability is the ratio of the number of times an outcome occurs to the total number of times the activity is performed,

`Pr_(experimental)=\frac{\text{number of times an outcome occurs}}{\text{total number of times the activity is performed}}.`

3. In your case, the experimental probability (from the table) is

`Pr_(experimental)=(1)/(5).`

Note that a bag contains 5 tiles in total, one yellow tile among them, then

• number of favorable outcomes = 1;
• number of all possible outcomes = 5

and

`Pr_(theoretical)=(1)/(5).`

Thus, the experimental probability is the same as the theoretical probability

Answer 2

The experimental probability is the same as the theoretical probability.

Explanation:

Theoretical probability of a yellow tile 1/5

1/5 * 50 trials = 10 yellow tiles should be drawn