Question

You and a friend are playing a game of chance. Every time you roll (using a fair die) a 1, 2, 3, or 4, you are successful, and your friend will pay you $1. Every time you roll a 5 or 6, you must pay your friend $2. If 65% of your rolls are successful and 35% of your rolls are unsuccessful, how much money do you expect to have won/owe by the end of the game?

You owe 41 cents

You have won 5 cents

You owe 5 cents

You have won 41 cents

Answer 1

you owe $5

Explanation:

65% wins means $65

35% losses means -$70

Answer 2

You owe 5 cents.

Explanation:

(the amount of money won)(the number of successful rolls)+(the amount of money lost)(the number of unsuccessful rolls)=expected value

65% of rolls are successful which means that 13/20 of the rolls are successful (simply convert to a fraction).

35% of the rolls are unsuccessful which means that 7/20 of the rolls are unsuccessful.

Using the equation above we can use,

(1)(13/20)+(-2)(7/20)

to find the expected value.

(1)(13/20)+(-2)(7/20)=0.05