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Chapter 4: Problem 23

Three dice are tossed. How many simple events are in the sample space?

Short Answer

Expert verified
Answer: There are 216 simple events in the sample space when three dice are tossed.

Step by step solution

01

Determine the number of possible outcomes for each die

Since a die has 6 faces, each with a different number ranging from 1 to 6, there are 6 possible outcomes for each die.
02

Calculate the total number of outcomes for three dice

To calculate the total number of outcomes for three dice, we will use the multiplication principle, which states that if there are m ways to perform one operation and n ways to perform another operation, then there are m*n ways to perform both operations. In this case, there are 6 possible outcomes for each die, so there are 6*6*6=216 possible ways to combine the outcomes from all three dice.
03

Determine the number of simple events in the sample space

In this exercise, a simple event is a single combination of outcomes from all three dice. Since there are 216 possible combinations of outcomes for the three dice (as calculated in Step 2), there are 216 simple events in the sample space. So, we can conclude that there are 216 simple events in the sample space when three dice are tossed.

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