Question

Suppoose you pay $3 to roll a fair die with the understanding that you will get back $9.00 if you roll a 1 or a 6 but nothing otherwise. What are your expecfted winnings?

Answer 1

There is a 33.33% that you will roll a 1 or a 6.

Answer 2

Expected winnings are

9* 1/6 + 0 * 1/6 + 0*1/6 + 0*1/6 + 0 * 1/6 + 9 * 1/6

9/6+9/6 = 18/6 = 3

Earnings: winnings - cost

3-3 = 0