A square dart board has four dark circular regions of radius 3 inches

Hello, everyone. For those who may want to get to the answer a little quicker, you can reduce the fraction without multiplying everything out first. That is, you can think of the probability in the following way:

\(P=\frac{(4*π*3^2)}{(24*24)}\)

\(P=\frac{36π}{(24*24)}\)

\(P=\frac{(12*3)π}{((12*2)*(8*3))}\)

\(P=\frac{π}{(2*8)}\)

\(P=\frac{π}{16}\)

The answer must be (A). You can practice such a question mentally, without writing down any numbers, although I would not advise doing so on the test. With a little knowledge of factoring, the question should take about a minute, and you could spend that extra time on a tougher question that may warrant it.

Good luck with your studies.

- Andrew

Solution:

The probability that a dart that hits the dart board will hit one of the circular regions is the combined area of the 4 circular regions divided by the area of the dart board.

The combined area of the 4 circular regions is 4 x (π x 3^2) = 36π square inches.

The area of the dart board is 24^2 = 576 square inches.

Therefore, the desired probability is 36π/576 = π/16.

Answer: A