Lesson 3
What Are Probabilities?
Let’s find out what's possible.
Problem 1
List the sample space for each chance experiment.
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Flipping a coin
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Selecting a random season of the year
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Selecting a random day of the week
Problem 2
A computer randomly selects a letter from the alphabet.
- How many different outcomes are in the sample space?
- What is the probability the computer produces the first letter of your first name?
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.
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.
- What does the \(\frac16\) represent in this situation?
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Give an example of what a person might weigh on Earth and on the Moon.
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.](https://staging-cms-im.s3.amazonaws.com/zqXQwkWmu3PCz56sNcz8dy5U?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP_Image_13abcd.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP_Image_13abcd.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143439Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c46e98d14006e94586486371a5ecaa56066f6011880181074bf2e76dee801e31)
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.](https://staging-cms-im.s3.amazonaws.com/QCnEtUnfQZmzH2B3JfbRydLv?response-content-disposition=inline%3B%20filename%3D%227-7.6.C.PP.Image.13.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.C.PP.Image.13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143439Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=89dc834b7b1763ff5645c5545a7574c2959691e437a6d7c498014ea3a687fe77)