Question

if a standard six - sided die is rolled, what is the theoretical probability of getting a number greater than 4?
○ 1/6
○ 1/3
○ 2/3
○ 1/2
question 17
5 pts
which of the following statements best describes the difference between theoretical and experimental probability?
○ theoretical probability is based on expected outcomes, while experimental probability is based on actual results from an experiment.
○ experimental probability is always equal to theoretical probability.
○ theoretical probability is always higher than experimental probability.
○ experimental probability is based on predictions, not actual results.

Explanation:

First Question (Probability of rolling a number >4 on a six - sided die)

Step 1: Identify total and favorable outcomes

A standard six - sided die has 6 possible outcomes: 1, 2, 3, 4, 5, 6. The numbers greater than 4 are 5 and 6, so there are 2 favorable outcomes.

Step 2: Calculate probability

The formula for probability is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Substituting the values, we get $P = \frac{2}{6}=\frac{1}{3}$.

• Option 1: Theoretical probability uses the formula $\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ (expected outcomes), and experimental probability is calculated as $\frac{\text{Number of times event occurs}}{\text{Total number of trials}}$ (actual results from experiments). This is correct.
• Option 2: Experimental probability is not always equal to theoretical probability. For example, in a few coin flips, the number of heads may not match the theoretical 0.5 probability. So this is wrong.
• Option 3: Theoretical probability is not always higher than experimental probability. It can be lower or equal depending on the experiment. So this is wrong.
• Option 4: Experimental probability is based on actual results, not predictions. Theoretical probability is based on predictions (expected outcomes). So this is wrong.

Answer:

$\frac{1}{3}$ (corresponding to the option "1/3")

Second Question (Difference between theoretical and experimental probability)