Stats word probability problem

Question

If possible, please assist me with the formula and finding the answer please!

 

In a simple game, a six-sided die is rolled 4 times. If all four rolls result in either 1 or 2, then the player wins $50 dollars. If the player has to pay $10 to play the game, what are the expected winnings of the player over time if many games are played?

Answer 1

The probability of getting a 1 or a 2 on each roll is 2/6 = 1/3.

 

Since each roll is independent, the probability of getting a 1 or a 2 on all 4 rolls is (1/3)⁴ = 1/81.

 

So he has a 1 in 81 chance of winning $50.  So the expected value of each game is $50 / 81 = $0.62.

 

If he has to pay $10 to win $0.62, then he is going to lose money quickly.