A six-sided die is rolled 60 times in an experiment. The results are:



1: 8 times


2: 12 times


3: 10 times


4: 10 times


5: 9 times


6: 11 times


How does the experimental probability of rolling a 1 compare to the theoretical probability?
(4 Points)

The experimental probability (8/60) is less than the theoretical probability (1/6).

The experimental probability (8/60) is equal to the theoretical probability (1/6).

The experimental probability (8/60) is greater than the theoretical probability (1/6).

There is no way to compare experimental and theoretical probability.

1 answer

To compare the experimental probability of rolling a 1 to the theoretical probability, we need to calculate the experimental probability first.

The experimental probability of rolling a 1 is calculated as follows:

\[ \text{Experimental Probability of rolling a 1} = \frac{\text{Number of times 1 was rolled}}{\text{Total number of rolls}} = \frac{8}{60} \]

Now, we can simplify \( \frac{8}{60} \):

\[ \frac{8}{60} = \frac{2}{15} \approx 0.1333 \]

Next, we find the theoretical probability of rolling a 1 with a fair six-sided die. The theoretical probability is:

\[ \text{Theoretical Probability of rolling a 1} = \frac{1}{6} \approx 0.1667 \]

Now we can compare the two probabilities:

  • Experimental Probability of rolling a 1 = \( \frac{2}{15} \approx 0.1333 \)
  • Theoretical Probability of rolling a 1 = \( \frac{1}{6} \approx 0.1667 \)

Since \( 0.1333 < 0.1667 \), we can conclude that:

The experimental probability (8/60) is less than the theoretical probability (1/6).