MATH SOLVE

2 months ago

Q:
# The large square below has a side length of 8 inches, and the smaller white square inside the large square has a side length of 2 inches. mc020-1.jpg What is the probability that a point chosen at random is in the blue region?

Accepted Solution

A:

The image is not attached with, but by reading the question it is obvious that the blue region lies inside the larger square and outside the smaller square. That is the region between the two squares is the blue region.

We know the dimensions of both squares, using which we can find the area of both squares. Subtracting the area of smaller square from larger one, we can find the area of blue square and further we can find the said probability.

Area of larger square = 8 x 8 = 64 in²

Area of smaller square = 2 x 2 = 4 in²

Area of blue region = 64 - 4 = 60 in²

The probability that a randomly chosen point lies within the blue region = Area of blue region/Total area available

Therefore, the probability that a point chosen at random is in the blue region = 60/64 = 0.9375

We know the dimensions of both squares, using which we can find the area of both squares. Subtracting the area of smaller square from larger one, we can find the area of blue square and further we can find the said probability.

Area of larger square = 8 x 8 = 64 in²

Area of smaller square = 2 x 2 = 4 in²

Area of blue region = 64 - 4 = 60 in²

The probability that a randomly chosen point lies within the blue region = Area of blue region/Total area available

Therefore, the probability that a point chosen at random is in the blue region = 60/64 = 0.9375