Question

a game involves rolling a number cube. you get one point if you roll an even number and negative one point if you roll an odd number. which statements are true regarding this scenario? choose three correct answers. the expected value for the game is 0 the game is fair because the expected value is equal to 0

Explanation:

Step1: Calculate expected value

The formula for expected value \(E(X)=\sum_{i}x_ip_i\).
For roll \(1\): \(x_1=- 1,p_1=\frac{1}{6}\); roll \(2\): \(x_2 = 1,p_2=\frac{1}{6}\); roll \(3\): \(x_3=-1,p_3=\frac{1}{6}\); roll \(4\): \(x_4 = 1,p_4=\frac{1}{6}\); roll \(5\): \(x_5=-1,p_5=\frac{1}{6}\); roll \(6\): \(x_6 = 1,p_6=\frac{1}{6}\).

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Step2: Determine fairness

A game is fair if the expected value \(E(X) = 0\). Since \(E(X)=0\) for this game, it is fair.

Answer:

The expected value for the game is \(0\), The game is fair because the expected value is equal to \(0\)