A red die and a blue die are thrown. Let S be a random variable that denotes the square of the difference between the two numbers on the dice. For example, if the red die comes up 2 and the blue die comes up 5, then E(x):

E(x) = 5.83

Step-by-step explanation:

There are 36 possible outcomes.

There is a 6 in 36 chance that the difference between the dice is zero (square is also zero):

{1,1} {2,2} {3,3} {4,4} {5,5} {6,6}

There is a 10 in 36 chance that the difference between the dice is one (square is also 1):

{1,2} {2,1} {2,3} {3,2} {3,4} {4,3} {4,5} {5,4} {5,6} {6,5}

There is a 8 in 36 chance that the difference between the dice is two (square is 4):

{1,3} {3,1} {2,4} {4,2} {3,5} {5,3} {4,6} {6,4}

There is a 6 in 36 chance that the difference between the dice is three (square is 9):

{1,4} {4,1} {2,5} {5,2} {3,6} {6,3}

There is a 4 in 36 chance that the difference between the dice is four (square is 16):

{1,5} {5,1} {2,6} {6,2}

There is a 2 in 36 chance that the difference between the dice is four (square is 25):

{1,6} {6,1}

Therefore, the expected value for X is:

The expected value is E(x) = 5.83

me

step-by-step explanation:

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.