Question

a number cube was rolled as part of an experiment. the results are displayed in the table below.

number	frequency
2	6
3	5
4	7
5	3
6	5

what is the best explanation of how to find the experimental probability of rolling a 3?
○ to find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. simplify if necessary.
○ to find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency (or the number three). simplify if necessary.
○ to find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of possible outcomes. simplify if necessary.
○ to find the experimental probability of rolling a three, write a ratio of the total number of trials to the number of possible outcomes. simplify if necessary.

to find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. simplify if necessary.

to find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency (or the number three). simplify if necessary.

to find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of possible outcomes. simplify if necessary.

to find the experimental probability of rolling a three, write a ratio of the total number of trials to the number of possible outcomes. simplify if necessary.

Explanation:

To determine the best explanation for finding the experimental probability of rolling a 3, we analyze the options:

Step 1: Recall Experimental Probability Formula

Experimental probability of an event is given by the ratio of the number of times the event occurs (frequency of the event) to the total number of trials (sum of all frequencies).

Step 2: Analyze the Table

The table shows the frequency of each number rolled:

• Number 1: Frequency = 4
• Number 2: Frequency = 6
• Number 3: Frequency = 5
• Number 4: Frequency = 7
• Number 5: Frequency = 3
• Number 6: Frequency = 5

Step 3: Calculate Total Number of Trials

Total trials = \( 4 + 6 + 5 + 7 + 3 + 5 = 30 \)

Step 4: Analyze Each Option

• Option 1: "To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary."

This matches the formula for experimental probability (frequency of 3 divided by total trials).

• Option 2: "To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of three. Simplify if necessary."

This is the reciprocal of the correct ratio (total trials / frequency of 3), which is incorrect.

• Option 3: "To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of results. Simplify if necessary."

"Total number of results" is ambiguous and not the standard definition (we use total trials, not "results" in this context).

• Option 4: "To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number of sides. Simplify if necessary."

The number of sides (6) is irrelevant for experimental probability (which depends on actual trials, not theoretical sides).

Step 1: Recall Experimental Probability

Experimental probability = \( \frac{\text{Frequency of event}}{\text{Total number of trials}} \).

Step 2: Identify Event and Trials

• Event: Rolling a 3 (frequency = 5).
• Total trials: Sum of all frequencies = \( 4 + 6 + 5 + 7 + 3 + 5 = 30 \).

Step 3: Evaluate Options

Only the first option correctly uses \( \frac{\text{Frequency of 3}}{\text{Total trials}} \) to calculate experimental probability.

Answer:

The best explanation is: "To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary." (Corresponding to the first option in the list)