Probability and Geometry Problems Worksheet

Objective: I know how to solve probability problems that involve geometry.

Probability can also relate to the areas of geometric shapes. The following are some probability problems that involve areas of geometric shapes.

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

Work out the following.

1. A dart is thrown at random onto a board that has the shape of a circle as shown below.

Calculate the probability that the dart will hit the shaded region. (Use π = )

2. The figure shows a circle divided into sectors of different colours.
If a point is selected at random in the circle, calculate the probability that it lies:
a) in the red sector.

b) in the green sector.

c) in the blue sector.

d) in any sector except the green sector.

3. The figure shows a circle with centre O and radius 8 cm. ∠ BOD = 72°. The radius of the smaller circle is 4 cm. A point is selected at random inside the larger circle BCDE.

Calculate the probability that the point lies
a) inside the sector BODC.

b) inside the smaller circle

c) neither in the sector BODC nor in the smaller circle.

4. In the figure below, PQRS is a rectangle, and A, B, C, D are the midpoints of the respective sides as shown.

An arrow is shot at random onto the rectangle PQRS. Calculate the probability that the arrow strikes:
a) triangle AQB.

c) either triangle BRC or the unshaded region.

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