If a 6, 7, or 8 shows up on a roll of a pair of dice, you win two dollars. If anything else shows up, you lose one dollar. If you roll the dice 300 times, what is your expected amount of winnings?
+23246 Of the 36 possible combinations of the rolling of two dice
a 6 can appear 5 ways
a 7 can appear 6 ways
an 8 can appear 5 ways.
So, there is a total of 5 + 6 + 5 = 16 ways to win out of the 36 possibilities.
Probability of winning: 16/36.
This means that there are 36 - 16 = 20 ways to lose.
Probability of losing: 20/36
Expected winnings: 300 x [ 16/36 x $2.00 - 20/36 x $1.00 ] = .....
