Question

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.

An unshaded square inside of a large blue square.

What is the probability that a point chosen at random is in the blue region?
StartFraction 1 over 16 EndFraction
StartFraction 1 over 15 EndFraction
StartFraction 15 over 17 EndFraction
StartFraction 15 over 16 EndFraction

Answer 1

letter b Explanation:

Answer 2

The probability that a point chosen at random is in the blue region is 15/16.

Explanation:

In order to find the probability that a point chosen at random will lie in the blue region, we first have to find the area of the blue region.

The area
`A` of the large square is the product of its dimensions:

`A=(8in)^2=64in^2`

and for the smaller square area
`a` is:

`a=(2in)^2=4in^2`

Therefore the area of the blue region is the area of the larger square minus the area of the smaller square.

`A_(blue)=A-a=64in^2-4in^2=60in^2`

Therefore the probability that the point chosen at random is on the blue region is

`(A_(blue))/(A) =(60)/(64) =(15)/(16)`

The probability is
`15/16`.