Dice game probability

Question

Michael roles a single die. If you rolls a one or two, he wins $3 and if he roles a 3,4, or 5, he wins $2. However if he rolls a 6, he losss $11. Determine his expectation from a single roll of the die.

Answer 1

Event Value Probability

1 or 2 $3 1/3

3,4,5 $2 1/2

6 -$11 1/6

expectation = sum of (value * probability) = $3 * 1/3 + $2 * 1/2 + -11$ * 1/6 = $0.16