Grace and her friends are playing a game that uses two dice. Each die is a tetrahedron – a four‐sided shape with each side an equilateral triangle. Each side of the die contains
one of the digits 1, 2, 3, or 4.
a. Create the sample space of all possible outcomes if you were to roll the two dice
simultaneously. List the digit on the first die first and the digit on the second die
second (i. e. 1,1; 1,2; and so on.) (10 points)
b. What is the theoretical probability that the sum of the two numbers on a roll will
be five? (2 points)
c. If Grace and her friends were to roll the two dice 100 times, how many of the
100 times could they expect to roll the same number on each die? (In other
words, the outcome would be 1,1 or 2,2 or 3,3 or 4,4.) (4 points)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be