Make a table in which you list all possible outcomes of...

Make a table in which you list all possible outcomes of rolling two dice. Call the dice A and B. What is the probability of rolling (a) a $7,$ (b) any double, and (c) a 6 or an 87 You can give the probabilities as fractions, such as $3 / 36.$

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Key Concepts

Sample Space

The sample space in rolling two dice is the set of all possible ordered pairs representing the outcomes for each die. With one die having 6 faces, the total number of outcomes is 36, making it an essential foundation for probability calculations.

Outcome Table

Constructing a table that lists all possible ordered pairs for the two dice is a systematic method to visualize and ensure all outcomes are considered. This approach aids in accurately counting favorable outcomes for any event.

Counting Favorable Outcomes

Counting the number of outcomes that satisfy a specific event, such as the sum of the dice equaling 7 or both dice showing the same number (doubles), is key. By evaluating the outcome table, one can determine the numerator in the probability fraction.

Probability Calculation

Probability is determined by dividing the number of favorable outcomes by the total number of outcomes in the sample space. Representing probabilities as fractions (like 3/36) lays the groundwork for comparisons and further computations in probability.

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