SOLUTION: My homework is on geometric probability. One of my problems has to do with a dart board. I am given that the Diameter of the outer double ring = 41 cm. the diameter of the inner do

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Question 255171: My homework is on geometric probability. One of my problems has to do with a dart board. I am given that the Diameter of the outer double ring = 41 cm. the diameter of the inner double ring = 36 cm. the diameter of the outer triple ring = 25.6 cm. the diamter of the inner triple ring = 21.2 cm. the diamer of the outer bulls eye = 4.4 cm. and finally the diameter of the inner bull's eye = 1.4 cm. My question asks What is A) what is the probability that the dart will land IN the double ring B) What is the probability of hitting the single bull's eye and finally C) what is the probability of hitting the triple 20 ring. Please help as much as possible, I'd really appreciate it. Thank you!
Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
First find the area of each ring or section. You can so this in each case by finding the area of the circle whose circumference is the outer part of the ring and substract the area of the circle whose circumference is the inner part of the ring. The formula for the area of a circle is A = pi*r^2 where r (the radius) is 1/2 of the diameter.
Once you have the area of each ring (or section) the probability of a dart landing in that ring or section is given by the area of the ring or section divided by the area of the entire dart board (that is, the percent the ring or section represents of the total area of the dart board).
Note that we have assumed that a dart would always hit somewhere on the dart board and also that each individual "point" on the board was equally likely to be hit by random throw :)