A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.22, the probabil
ity that a roll comes up 1 or 2 is 0.42, and the probability that a roll comes up 2 or 3 is 0.54 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)
Since the probability of rolling a 1 is 0.22 and the probability of rolling either a 1 or a 2 is 0.42, the probability of rolling only a 2 can be determined as:
The same logic can be applied to find the probability of rolling a 3
The sum of all probabilities must equal 1.00, so the probability of rolling a 4 is:
The expected winnings (EW) is found by adding the product of each value by its likelihood:
you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.
