SOLUTION: On two rolls of a single die, you will lose $10 if a 4 turns up at least once, and you will win $3 otherwise. What is the expected value of the game?

Question 747801: On two rolls of a single die, you will lose $10 if a 4 turns up at least once, and you will win $3 otherwise. What is the expected value of the game?

Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
The chance of a 4 is 1 in 6.
In the 36 possible combinations, 6 times a 4 will be first, and 6 times a 4 will be second, so 12 rolls out of 36. But one of these are double counted, the 4,4 outcome. So it's really 11 rolls that contain a 4. The remaining 25 outcomes contain no 4.
11 * -$10 = -$110
25 * $3 = $75
36 rolls produce -$35, or -$0.97 per roll.
RELATED QUESTIONS
Having problems understanding Random Variable, Probability Distribution and Expected... (answered by stanbon)

a friend offers the following game: she wins $1 from you if, on 2 rolls of a single die,... (answered by jorel555)

A friend offers the following game. She wins $1 from you if, on four rolls of a single... (answered by Boreal)

the carnival has come to town, and lucky Louie has once again set up his pavilion.he... (answered by stanbon)

A certain game consists of rolling a single fair die. If a four or five comes up,... (answered by math_helper)

Suppose you roll a die 3 times. What is the probability that the face 6 will show up at... (answered by edjones)

If a fair die rolled once comes up 6 you win $100. Otherwise, you lose $15. Would a... (answered by stanbon)

In the carnival game "chuck-a-luck," you pick a number from 1 to 6 and roll 3 dice in... (answered by stanbon)

In a dice game, you roll a dice once for a $5 wager. You win $8.00 for rolling a 3 or a... (answered by Edwin McCravy)