Lesson: Using Lengths and Areas to Find Geometric Probability

Alice is randomly tossing shoes onto her rug which is modelled in the diagram. What is the probability that the shoes will land in the shaded area of the rug? Give your answer as a fraction in its simplest form.

At an animal park, the keeper feeds the lion at a random time between 2 and 3 pm for about 5 minutes. A family decides to go to the lion area at a random time between 2 and 3 pm and, in case the lion keeper has not started yet to feed the lions, to wait for 15 minutes for the keeper to arrive before leaving. What is the probability that the family sees the lions being fed?

A target board consists of three concentric circles of radii 6 cm, 12 cm, and 24 cm, which define three regions gold, red, and blue as shown in the diagram. If a dart is thrown randomly such that it hits the target, what is the probability that it will hit the red region?