A rectangular dartboard that measures 12 inches by 24 inches has a 2-inch by 2-inch red square painted at its center. What is the probability that a dart that hits the dartboard will land in the red square?
Sometimes we need to use our knowledge of geometry to determine the likelihood of an event occurring. We may use areas, volumes, angles, polygons or circles.
Let's solve the following problems.
- A game of pin-the-tale-on-the-donkey has a rectangular poster that is 2ft by 2ft. The area in which the tale should be pinned is shown as a circle with radius 1 inch. Assuming that the pinning of the tale is completely random and that it will be pinned on the poster (or the player gets another try), find the probability of pinning the tale in the circle?
This probability can be found by dividing the area of the circle target by the area of the poster. We must have the same units of measure for each area so we will convert the feet to inches.
- In a game of chance, a pebble is dropped onto the board shown below. If the radius of each of blue circle is 1 cm, find the probability that the pebble will land in a blue circle.
- What is the probability that a randomly thrown dart will land in a red area on the dart board shown? What is the probability that exactly two of three shots will land in the red? The radius of the inner circle is 1 unit and the radius of each annulus is 1 unit as well.
Earlier, you were asked to find the probability that a dart that hits the dartboard will land in the red square.
Therefore, there is about a 1.39% chance the dart will hit the red square.
Consider the picture below. If a “circle” is randomly chosen, what is the probability that it will be:
- blue or green
- not orange
If a dart is randomly thrown at the target below, find the probability of the dart hitting in each of the regions and show that the sum of these probabilities is 1. The diameter of the center circle is 4 cm and the diameter of the outer circle is 10 cm. What is the probability that in 5 shots, at least two will land in the 4 region?
Now add them up:
Use binomial probability to determine these probabilities:
Use the diagram below to find the probability that a randomly dropped object would land in a triangle of a particular color.
- not yellow
- not yellow or light blue
- Given a random throw of a dart, what is the probability that it will land in a white ring?
- What is the probability of a bull’s eye?
- What is the probability that in 10 throws, exactly 6 land in the black regions?
- What is the probability that in 10 throws, at least one will land in the bull’s eye?
- How many darts must be thrown to have a 95% chance of making a bull’s eye?
Answers for Review Problems
To see the Review answers, open this PDF file and look for section 12.11.