A red die and a blue die are rolled. You win or lose money depending on the sum of the values of the two dice. If the sum is 6 or 10, you win $4. If the sum is 5, 9, or 12, you win $1. If the sum is any other value (2, 3, 4, 7, 8, or 11), you lose $2. Let X be a random variable that corresponds to your net winnings in dollars. What is the expected value of X

The expected value of X is $0.0833.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

For each dice, there are 6 possible outcomes(values from 1 to 6). So for 2 dices, there are desired outcomes.

Desired outcomes:

Sum 5: (1,4), (2,3), (3,2), (4,1).

Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)

Sum of 9: (3,6), (4,5), (5,4), (6,3)

Sum of 10: (4,6), (5,5), (6,4)

Sum of 12: (6,6)

Probabilities:

5 + 3 = 8 outcomes in which the sum is 6 or 10, that is, 8/36 probability of winning $4.

4 + 4 + 1 = 9 outcomes in which the 5, 9, or 12, that is, 9/36 probability of winning $1.

36 - (8 + 9) = 36 - 17 = 19 remaining outcomes, that is, 19/36 probability of losing $2.

What is the expected value of X?

Multiplication of each outcome by its probability. So

The expected value of X is $0.0833.

no

step-by-step explanation:

2-7=-5

7-2=5

when you combing like terms for ech expression, 5 and -5. these numbers are not equal to each other.

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.