There’s a game where you are asked to roll two fair six-sided dice. If the sum of the values on the dice equals seven, then you win $21. However, you must pay $5 to play each time you roll both dice. Do you play this game? And in the follow-up: If he plays 6 times what is the probability of making money from this game?
The first condition states that if the sum of the values on the 2 dices is equal to 7, then you win $21. But for all the other cases you must pay $5.
First, let’s calculate the number of possible cases. Since we have two 6-sided dices, the total number of cases => 6*6 = 36.
Out of 36 cases, we must calculate the number of cases that produces a sum of 7 (in such a way that the sum of the values on the 2 dices is equal to 7)
Possible combinations that produce a sum of 7 is, (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1). All these 6 combinations generate a sum of 7.
This means that out of 36 chances, only 6 will produce a sum of 7. On taking the ratio, we get: 6/36 = 1/6
So this suggests that we have a chance of winning $21, once in 6 games.
So to answer the question if a person plays 6 times, he will win one game of $21, whereas for the other 5 games he will have to pay $5 each, which is $25 for all five games. Therefore, he will face a loss because he wins $21 but ends up paying $25.