a The yellow and blue regions form a circle. Use the area of this circle to find the probability of the dart landing there.
B
b The probability of not hitting the gray region is the same as the probability of the dart hitting any of the regions of other colors.
A
a π/36 or about 8.7 %.
B
b π/16 or about 19.6 %
Practice makes perfect
a To find the probability of hitting a certain region of a dart board, we need to find the ratio of the area of the desired region to the area of the board. Let's look at our given dimensions.
Together, the blue and yellow regions form a circle with a radius of 2. We can use this to find the area of the circle created by the blue and yellow regions.
Therefore, the probability of the dart that hits the board at a random point will hit the yellow or blue regions is π36 or about 8.7 %.
b The probability that it will not hit the gray region is the same as the probability that it will hit the circular regions. Therefore, we need to find the area of the entire circular region formed by the blue, yellow and red regions.
In Part A, we determined that the radius of the innermost blue circle is 1 inch. Therefore, the radius of the circle formed by the blue, yellow, and red regions is 1+1+1=3 inches. Let's find the area of that circle.
A_(Circle)&=Ď€ * 3^2
&= 9 π
Now, we can look at the ratio of the circle's area to that of the entire square. We determined the area of the square in Part A was 144 in^2.
