Rolling the Dice An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The following frequency histogram gives the results.

a. What was the most frequent outcome of the experiment?
b. What was the least frequent?

Verified step by step guidance

1. Step 1: Understand the histogram. The x-axis represents the possible sums when two dice are rolled (from 2 to 12), and the y-axis shows the frequency of each sum occurring in 100 rolls.
2. Step 2: Identify the most frequent outcome by looking for the tallest bar in the histogram. The height of each bar corresponds to how many times that sum appeared.
3. Step 3: Identify the least frequent outcome by finding the shortest bar in the histogram, which represents the sum that appeared the fewest times.
4. Step 4: Note the values on the x-axis corresponding to these tallest and shortest bars to determine the sums for the most and least frequent outcomes.
5. Step 5: Use these observations to answer the questions: the most frequent outcome is the sum with the highest frequency, and the least frequent outcome is the sum with the lowest frequency.

Key Concepts

Frequency Distribution

A frequency distribution shows how often each outcome occurs in a data set. In this experiment, it displays how many times each possible sum of two dice appeared in 100 rolls, helping identify the most and least common sums.

Sum of Two Dice Outcomes

When rolling two dice, the possible sums range from 2 to 12. Each sum has a different probability based on the number of dice combinations that produce it, with 7 being the most likely sum due to the highest number of combinations.

Interpreting Histograms

A histogram visually represents data frequencies using bars. The height of each bar corresponds to the frequency of each sum, allowing quick identification of the most and least frequent outcomes in the experiment.