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Chapter 11: Problem 20

What does the expected value for the outcome of the roll of a fair die represent?

Short Answer

Expert verified
The expected value for the outcome of the roll of a fair die is 3.5. It represents the average outcome if we roll the die many times.

Step by step solution

01

Understand the concept

The concept of 'Expected Value' in probability is essentially a weighted average of all possible values that a random variable can take, with each value being weighted by the probability of that event occurring. In the case of a fair die, the events are the outcomes of each roll (1, 2, 3, 4, 5, 6) and each has an equal probability of 1/6.
02

Express the expected value formula

The formula for the expected value (E) is given by: \[ E(X) = \sum_{i=1}^{n} x_i * P(x_i) \] Where: \(n\) is the number of possible outcomes, \(x_i\) is each possible outcome, \(P(x_i)\) is the probability of each outcome.
03

Calculate the expected value

Substitute each outcome of the die roll and its corresponding probability into the formula. Therefore, the expected value for the roll of a fair die would be: \[ E(X) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5 \]

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