Worksheet Materials (Student Handout)
2-page printable question handout for students

 

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Worksheet Materials (Answer Handout)
4-page printable answer page for teachers

 

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Materials for Offline Use (na)
  • Currently spinner activity is freely available online, but costs money to purchase and use offline.
Metadata
Brief User considers real-life problem of cost/reward of cereal box prizes. Determines corresponding circle graph and constructs interactive spinner. Tests results to see comparison between theoretical and experimental probabilities. Applies algebra to determine real-life cost/benefit.
Pre-knowledge Basic probability skills.
Goal Understanding theoretical and experimental probability, real-life situations
Grade 8-10 (8th grade, pre-algebra, probability & statistics)
Strand Statistics, Data Analysis and Probability; Algebra and Functions
Standards CA 6.SP.3.3,  CA Probability 1.0,  CA Probability 3.0, ACT PS 20-23
Keywords probability, statistics, real-life, circle graph, spinner, interactivity, theoretical, experimental  
Comments Suitable for 8th-grade on up.
Source Lana Steckler-Marshall and Linda Fahlberg-Stojanovska (no copyright)

For the Probability Reasoning Workshop from the MathForum

Cost Activity and software is free to use
Download Currently spinner activity is freely available online and costs money to purchase and use offline.
Type Java Applet so requires free sunJava player
Cereal Box Problem    by Lana Steckler-Marshall & Linda Fahlberg-Stojanovska  
For the Probability Reasoning Workshop from the MathForum

Problem setting: A cereal company has a new advertising campaign.

Inside 1/6 of all cereal boxes is a $2.00 cash prize.
Inside 1/3 of all boxes is a small toy.
No box contains two prizes.

Questions:

a) What is the probability of opening a box and receiving no prize?

Probability of no prize:

b) If you purchased 10 boxes, how many boxes should contain something (cash or toy)?

Approximately how many should contain cash? Why?

Approximately how many should contain a toy? Why?

Answer 1:

Answer 2:

Answer 3:

c) Click this link: NLVM Spinner.

Use CHANGE SPINNER and make a spinner that BEST represents the set of probabilities.

----

Check with your teacher to be sure you chose the correct spinner!

Help Setting up Spinner

   

d) Spin the spinner 10 times. Record your results: number of times cash is won, number of times a toy is won.
Does your answer agree with your answer to question b? Must it?

 
d  

 
 

   
e  

 

   
f  

 
 

   
 

 

     

e) If a box of cereal costs $4.00 and the cash prize is $2.00, how much did you spend to purchase the 10 boxes of cereal? How much did you earn? How many toys did you find?

f) Repeat steps (d) and (e) 9 more times. Following the 100 spins, determine:

What was the total amount of money earned?

How many toys did you find? If each toy is worth $0.50, what cash value of toys did you earn?

How to do multiple spins?

   

g) Before this new advertising campaign: It cost the company $1.50 for each box of cereal that it made and they usually sold each box for $3.50.
What was their profit for 100 boxes?
Old profit is:
h) During this new advertising campaign: It costs the company $1.50 for each box of cereal that it makes, and they now sell the cereal for $4.00.
What is their profit for 100 boxes -- taking into consideration the total value of the cash prizes and toys in these 100 boxes (use your totals from part (f))?
New profit is:
i) Based on your answers for (g) and (h), will this new campaign boost profits for the cereal company if the number of customers who purchase this cereal does not change? Why or why not?  
New campaign

profitable

New campaign

not profitable

j) Why might your answer be different from the person next to you?
Explanation:

Related themes:


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Page last modified on May 01, 2008, at 08:32 AM