I think this is geometry: There is a small box with a black frame around it. Inside the box, at the bottom, is an 8. Inside the box, to the right, is a 2. It looks like they are showing Length & Height. On the outside of the box, under the 8, there is a 10. To the right, outside the box, there is a 4. The question is: If a point is selected at random in the drawing shown, what is the probability that it would lie within the shaded region? 40%, 50%, 60%, or 70%?

I am an amateur, so my answer might not be correct.

If I understand this right, you are talking about a non-shaded box, 8x2, inside a larger, shaded box, 10x4. The area of the inner box is 16. The area of the outer box, 40.

40/100 = 16/x
x = 1600/40
x = 40

The area of the inner box is 40% of the outer box. So I think the correct answer is there is a 60% chance a random point would lie outside the smaller box, and inside the larger box.

As I remember, probability is not given as a percent, but as a number between 0 and 1. So the probability that the point would lie outside the smaller box, and inside the larger box is 0.6. But that is not one of the choices for an answer. So it looks to me like the question should be "What is the chance that it would lie within the shaded region".