Lesson 3

What Are Probabilities?

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Problem 1

List the sample space for each chance experiment.

  1. Flipping a coin

  2. Selecting a random season of the year

  3. Selecting a random day of the week

Solution

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Problem 2

A computer randomly selects a letter from the alphabet.

  1. How many different outcomes are in the sample space?
  2. What is the probability the computer produces the first letter of your first name?

Solution

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Problem 3

What is the probability of selecting a random month of the year and getting a month that starts with the letter “J?” If you get stuck, consider listing the sample space.

Solution

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Problem 4

\(E\) represents an object’s weight on Earth and \(M\) represents that same object’s weight on the Moon. The equation \(M = \frac16E\) represents the relationship between these quantities.

  1. What does the \(\frac16\) represent in this situation?

  2. Give an example of what a person might weigh on Earth and on the Moon.

Solution

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(From Unit 2, Lesson 4.)

Problem 5

Here is a diagram of the base of a bird feeder which is in the shape of a pentagonal prism. Each small square on the grid is 1 square inch.

The distance between the two bases is 8 inches. What will be the volume of the completed bird feeder?

diagram of the base of a bird feeder which is in the shape of a pentagonal prism. Each small square on the grid is 1 square inch.

 

Solution

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(From Unit 7, Lesson 13.)

Problem 6

Find the surface area of the triangular prism.

A triangular prism with a triangular base. The sides of the triangle have lengths of 3 and 4 units, and a hypotenuse with a length of 5 units. The height of the prism has a length of 4 units.

Solution

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(From Unit 7, Lesson 14.)