If 0

Question

If  0<x<4  and  0<y<4 , what is the probability that  x + y < 1  ?

A.  \frac{1}{2}

B.  \frac{1}{4}

C.  \frac{1}{8}

D.  \frac{1}{16}

E.  \frac{1}{32}

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gmatophobia · Accepted Answer

Given

0 < x < 4

0 < y < 4

Let's plot this over X-Y plane to see what is the 'total' region that needs to be considered. The area enclosed by the intersection of the two lines is the area of interest.

Also, we see that the intersection of the two lines forms a square OABC.

Total Area = area of square OABC = 4 * 4 = 16 units.

Now, we require to find the probability of x + y < 1

Let's plot x + y = 1 on the X-Y plane, the area below that line will represent x + y < 1

Plotting x + y = 1

y = -x + 1

X intercept (i.e. y =0) = (1,0)
 
 Y intercept (i.e. x =0) = (0,1)

We see that the intersection of x axis and y axis with the line x + y = 1 forms a triangle OMN in the X-Y plane.

As we need the probability of x + y < 1, the area enclosed by triangle OMN is the favorable area.

Favorable Area = Area of triangle OMN =  \frac{1}{2} * 1 * 1  =  \frac{1}{2}

Required Probability = Favorable Area / Total Area

=  \frac{1}{2} /16

=  \frac{1}{32}

Option E

mimundertaker · Answer

Could you please help with this question?

Bunuel · Answer

A solution is given  HERE . However, I doubt that such question could appear on new Focus edition tests. So, you can ignore it and move on.

If 0 < x < 4 and 0 < y < 4, what is the probability that x + y < 1 ?

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