A vehicle arriving at an intersection can turn right, turn left, or continue straight ahead. The experiment consists of observing the movement of a single vehicle through the intersection.
A) List the sample space for this experiment.
B) Assuming that all sample points are equally likely, find the probability that the vehicle turns.

a) Sample space (S) = {TR, TL, Cs}

b) Pr(Vehicle Turns) = 2/3.

Step-by-step explanation:

a) By sample space (S) we mean the list all possible outcome of an event. From the illustration in the question, only three (3) outcome is possible:

i) Vehicle Turn Right (TR)

ii) Vehicle Turn Left (TL)

iii) Continue Straight ahead (Cs)

And since the experiment consists of observing the movement of a single vehicle through the intersection, then, the sample space (S) is:

==> {TR, TL, Cs}

b) Since we are assuming that all sample points are equally likely, it imply that they have equal probability of occurring. And by probability:

Pr(TR) = 1/3

Pr(TL) = 1/3

Pr(Cs) = 1/3

Meanwhile, the question wants us to find the probability that the vehicle turns. This means, the vehicle turning either right or left. Thus;

Pr(vehicle turns) = Pr(TR) or Pr(TL) = Pr(TR) + Pr(TL)

Pr(vehicle turns) = (1/3) + (1/3) = 2/3

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