Lesson Worksheet: Geometric Probability Mathematics

In this worksheet, we will practice using lengths and areas to find geometric probability.

Q1:

What is the probability that the given fair spinner lands on a blue section?

  • A18
  • B14
  • C58
  • D12
  • E38

Q2:

Suppose three of the labeled points are chosen at random. What is the probability that the chosen points are collinear?

  • A1
  • B34
  • C12
  • D110
  • E0

Q3:

Suppose three of the labeled points are chosen at random. What is the probability that the chosen points are collinear?

  • A12
  • B34
  • C14
  • D1
  • E0

Q4:

A real number 𝑋 is randomly chosen between 10 and 100. Find the probability that 𝑋 is closer to 50 than to 100.

  • A49
  • B1318
  • C12
  • D59
  • E518

Q5:

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?

  • A12
  • B316
  • C14
  • D116

Q6:

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?

  • A43144
  • B716
  • C710
  • D101144
  • E916

Q7:

What is the probability that the given fair spinner lands on a yellow section?

  • A18
  • B14
  • C58
  • D12
  • E38

Q8:

Find the probability that a randomly chosen point lies inside the shaded part.

Q9:

A point within the square shown below is picked at random. In terms of 𝜋, find the probability that a randomly chosen point lies inside the circle.

  • A0.5𝜋
  • B0.25𝜋
  • C0.07𝜋
  • D𝜋
  • E0.75𝜋

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