See Problems 3 and 4.

A point in the figure is chosen at random. Find the probability that the point lies in the shaded region.

Target Game A target with a diameter of 14 cm has 4 scoring zones formed by concentric circles. The diameter of the center circle is 2 cm. The width of each ring is 2 cm. A dart hits the target at a random point. Find the probability that it will hit a point in the indicated region.

21. the center region
22. the blue region
23. either the blue or red region
24. any region

B Apply

25. Points M and N are on Z B ¯ z b bar  with M between Z and N. ZM = 5   , N B = 9   , equals 5 comma . n b equals 9 comma  and Z B = 20   . z b equals 20 .  A point on Z B ¯ z b bar  is chosen at random. What is the probability that the point is on M N ¯ ? m n bar , question mark
26. B Z ¯ b z bar  contains M N ¯ m n bar  and B Z = 20   . b z equals 20 .  A point on B Z ¯ b z bar  is chosen at random. The probability that the point is also on M N ¯ m n bar  is 0.3, or 30%. Find M N ¯ . m n bar , .
27. Think About a Plan Every 20 min from 4:00 p.m. to 7:00 p.m., a commuter train crosses Boston Road. For 3 min, a gate stops cars from crossing over the tracks as the train goes by. What is the probability that a motorist randomly arriving at the train crossing during this time interval will have to stop for a train?
    • How can you represent the situation visually?
    • What ratio can you use to solve the problem?
28. Reasoning Suppose a point in the regular pentagon is chosen at random. What is the probability that the point is not in the shaded region? Explain.

    

29. Commuting A bus arrives at a stop every 16 min and waits 3 min before leaving. What is the probability that a person arriving at the bus stop at a random time has to wait more than 10 min for a bus to leave?
30. Astronomy Meteorites (mostly dust-particle size) are continually bombarding Earth. The surface area of Earth is about 65.7 million mi 2 . mi squared , .  The area of the United States is about 3.7 million mi 2 . mi squared , .  What is the probability that a meteorite landing on Earth will land in the United States?
31. Reasoning What is the probability that a point chosen at random on the circumference of ⊙ circle dot  C lies on A B ⌢ ? modified eh b with frown above , question mark  Explain how you know.

    

32. Writing Describe a real-life situation in which you would use geometric probability.

Table of Contents