The most commonly used dice are six-sided, with numbers 1 through 6 on the faces. tom is playing a game in which he is rolling two six-sided dice. in the game, then, the smallest possible sum on the two dice is 2, and the largest possible sum is 12.

(a) what is the expected value of the sum of the two dice?

(b) what is the probability of rolling a sum of 8?

(c) what is the probability of rolling a sum of 12?

(d) what is the probability of rolling a sum smaller than 13?

(e) what is the probability of rolling a sum of 3 or 11?

Step-by-step explanation:

Given that Tom is playing a game in which he is rolling two six-sided dice.

The outcomes are 36, and sample space would be

(1,1) (1,2)...(1,6), (2,1),,,,,, (6,3)...(6,6)

a) The sum X can take values as

X23456789101112  

p    1/36     1/18     1/12     1/9      5/36     1/6      5/36     1/9      1/12     1/18     1/36  1        

xp    1/18     1/6      1/3      5/9      5/6  1   1/6  1   1/9  1            5/6     11/18     1/3  7        

So E(x) = 7

b) P(X=8) =

c)

d) P(X<13) = 1 (certain event)

e)

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3