Question

The figure below shows a shaded rectangular region inside a large rectangle:

A rectangle of length 10 units and width 5 units is shown. Inside this rectangle is another rectangle of length 6 units and width 3 units placed symmetrically inside the larger rectangle. The smaller rectangle is shaded gray.

What is the probability that a point chosen inside the large rectangle is not in the shaded region?

Answer 1

The correct answer is 64%.

The area of the large rectangle is 10(5) = 50 sq. units.

The area of the small rectangle is 6(3) = 18 sq. units.

This means that the probability that a point inside the large rectangle is inside the small rectangle is 18/50.

The probability that a point inside the large rectangle is not inside the small rectangle is 1-(18/50) = 32/50. 32/50 = 64%