Question

Consider a game in which a fair die is rolled. If the die comes up 1, the player wins $2. If the die comes up 2, the player wins $1. For all other outcomes, the player loses $1. What is the expected amount that the player wins or loses? Round to the nearest cent.

Answer 1

Answer:

Expected amount is loss of 0.167 $.

Step-by-step explanation:

Probability is the ratio of number of favorable outcome to total number of outcomes.

Total number of outcomes = 6, since the die has 6 faces.

$\texttt{Probability of getting 1 =}\frac{1}{6}\\\\\texttt{Probability of getting 2 =}\frac{1}{6}\\\\\texttt{Probability of getting numbers except 1 and 2 =}\frac{6-2}{6}=\frac{4}{6}=\frac{2}{3}$

If the die comes up 1, the player wins $2. If the die comes up 2, the player wins $1. For all other outcomes, the player loses $1.

Now we need to find expected amount that the player wins or loses.

Expected amount = ∑Probability of event x Winning or losing on that event

$\texttt{Expected amount =}\frac{1}{6}\times 2+\frac{1}{6}\times 1-\frac{2}{3}\times 1=\frac{2+1-4}{6}=\frac{-1}{6}=-0.167$

Expected amount is loss of 0.167 $.