Lesson 5
More Estimating Probabilities
Problem 1
What is the same about these two experiments? What is different?
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Selecting a letter at random from the word “ALABAMA”
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Selecting a letter at random from the word “LAMB”
Solution
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Problem 2
Andre picks a block out of a bag 60 times and notes that 43 of them were green.
- What should Andre estimate for the probability of picking out a green block from this bag?
- Mai looks in the bag and sees that there are 6 blocks in the bag. Should Andre change his estimate based on this information? If so, what should the new estimate be? If not, explain your reasoning.
Solution
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Problem 3
Han has a number cube that he suspects is not so standard.
- Han rolls the cube 100 times, and it lands on a six 40 times.
- Kiran rolls the cube 50 times, and it lands on a six 21 times.
- Lin rolls the cube 30 times, and it lands on a six 11 times.
Based on these results, is there evidence to help prove that this cube is not a standard number cube? Explain your reasoning.
Solution
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Problem 4
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages.
- What is the sample space for this experiment?
- What is the probability that you turn to page 45?
- What is the probability that you turn to an even numbered page?
- If you repeat this experiment 50 times, about how many times do you expect you will turn to an even numbered page?
Solution
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(From Unit 8, Lesson 3.)Problem 5
A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between \(A\) and \(B\) is 5 inches.
![A rectangular prism.](https://staging-cms-im.s3.amazonaws.com/YpP7JxkQF5js9PyDm3AkAFuz?response-content-disposition=inline%3B%20filename%3D%227-7.6.C.PP.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.C.PP.Image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20241222%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20241222T101027Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=80c8ed781a01fbe1a369c43c9beaad94ab9c01c1b67ce89c761c0f9a87a6de7c)
What is the surface area of the original rectangular prism? What is the total surface area of the two triangular prisms together?
Solution
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(From Unit 7, Lesson 15.)