Question

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $9.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?

Answer 1

Expected winnings are earnings minus cost

Earnings:

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

Winnings:

earnings - cost =3-3 = 0