expected value

Question

A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.12, the probability that a roll comes up 1 or 2 is 0.44, and the probability that a roll comes up 2 or 3 is 0.5 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)
Answer = dollars.

Answer 1

Set up a table, one column for value of the random variable and one for the probability"

 

x    P(x)

----------

1    .12

2    .32

3

4

 

Since each value is mutually exclusive I used P(1 or 2)=.44 and the fact that P(1)=.12 to calculate P(2).

Do something similar to get P(3). For P(4) use the fact that the sum of all the probabilities must add to 1.

 

Finally use the formula E(x)=Σxp(x) to calculate the expected value.

 

If you need more steps comment back.