two students created a game of dice. they determined that each roll would add the value of the die if it was…

two students created a game of dice. they determined that each roll would add the value of the die if it was an odd number. if the roll was even, it would subtract the value of the die. (for example, a roll of 2 would subtract two points, but a roll of 3 would add three points.) what is the expected value for this game?\n-3\n-0.5\n0\n0.5

two students created a game of dice. they determined that each roll would add the value of the die if it was an odd number. if the roll was even, it would subtract the value of the die. (for example, a roll of 2 would subtract two points, but a roll of 3 would add three points.) what is the expected value for this game?\n-3\n-0.5\n0\n0.5

Answer

Explanation:

Step1: List all possible outcomes

A die has 6 sides with values 1, 2, 3, 4, 5, 6. The probability of each outcome is $\frac{1}{6}$.

Step2: Determine the point - value for each outcome

For 1: add 1 point; for 2: subtract 2 points; for 3: add 3 points; for 4: subtract 4 points; for 5: add 5 points; for 6: subtract 6 points.

Step3: Calculate the expected - value formula

The expected value $E(X)=\sum_{i = 1}^{n}x_ip_i$, where $x_i$ is the outcome value and $p_i$ is the probability of the outcome. $E(X)=\frac{1}{6}(1-2 + 3-4 + 5-6)$

Step4: Simplify the expression

$E(X)=\frac{1}{6}(1 + 3+5-(2 + 4+6))=\frac{1}{6}(9 - 12)=\frac{1}{6}\times(-3)=-0.5$

Answer:

-0.5