Concept explainers
To find: The probability model for the total number of spots on two dice.
Answer to Problem 16E
Solution: The probability model for the total number of spots on two dice is given below.
Explanation of Solution
Calculation:
There are six spots on the six faces of a dice numbered from 1 to 6. So, when two dice are rolled, the possible outcomes or the
Each of the above outcomes is equally likely with probability
The total number of spots will have the following sample space:
The possible outcomes for each value of the total spots and the associated probabilities are as follows:
Since each outcome is independent, the individual probabilities are summed up.
The above probability model explains the total number of spots that can appear on the up-faces of two dice and the probability associated with them.
To find: The
Solution: The expected value of the total number of spots is 7.
Explanation:
Calculation:
The expected value of any discrete random variable X is computed by using the following formula:
where
So, by using the probability model obtained above and the formula of expectation, the expected value of the total number of spots is computed as follows:
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Chapter 20 Solutions
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