Find the probability of each event. Answer IN FRACTION form.

A bag contains five real diamonds and five fake diamonds. If five diamonds are picked from the bag at random, what is the probability that all of them are real?

So the idea is that we want to find the total number of ways that we can pick 7 diamonds (real or fake) from the 12 diamonds.

So as you said, 12 choose 7 = 792

Now we need the total number of ways that we can satisfy that of the 7 we picked, exactly three are real, but this also means that four are fake.

So to choose 3 real from 5 is 5 choose 3 = 10

And to choose 4 fake from 7 is 7 choose 4 = 35

3x10/792= 350/792= 175/396

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

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step-by-step explanation: