Question

a six - sided die was rolled 80 times. the number 3 was rolled 24 of those 80 times. the experimental probability of rolling a 3 is %, which is approximately % more than its theoretical probability. (round off your answers to the nearest integer.)

Explanation:

Step1: Calculate experimental probability

The experimental probability $P_{e}$ of an event is given by the formula $P_{e}=\frac{\text{Number of times the event occurred}}{\text{Total number of trials}}$. Here, the number of times 3 was rolled is 24 and the total number of trials is 80. So $P_{e}=\frac{24}{80}= 0.3$. To convert to a percentage, we multiply by 100, so the experimental - probability as a percentage is $0.3\times100 = 30\%$.

Step2: Calculate theoretical probability

For a fair six - sided die, the theoretical probability $P_{t}$ of rolling a 3 is $\frac{1}{6}\approx0.167$. To convert to a percentage, we multiply by 100, so $P_{t}=0.167\times100\approx17\%$.

Step3: Calculate the difference

The difference between the experimental and theoretical probabilities is $30 - 17=13\%$.

Answer:

30
13