Question

In a particular game of dice, you roll a single fair 6-sided die. You win 50 points for rolling a 1 or a 6, but you lose 5 points anytime you roll any other number. If you rolled the die 100 times, how many points would you expect to gain

or lose?
A. a gain of about 1,333 points
B. a gain of about 4,500 points
C. a loss of about 500 points
D. a gain of about 2,000 points

Answer 1

Answer: The expected value for rolling a 1 or 6 is 50 points, and the expected value for rolling any other number is -5 points. The chance of rolling a 1 or 6 is 2/6, or 1/3. The chance of rolling any other number is 4/6, or 2/3. The expected value for rolling the die once is:

(1/3 * 50) + (2/3 * -5) = 16.67

So, if you rolled the die 100 times, you would expect to gain or lose:

100 * 16.67 = 1667 points

The answer is: a gain of about 1,667 points.

Explanation: