Taste the Math (A Study In Probability)

Each pair of you will receive 1 pack of M & M’s and 1 pack of Skittles. Rip each bag open, poor out the M & M’s on one napkin and the Skittles on the other and let the math begin.

Part 1 (Collecting Sample Population Data)

Complete the Data Table below.

Skittles / M&M’s
Total
Red
Orange
Yellow
Green
Blue
Purple
Brown

Part 2 (Graphing using different representations)

  1. Create a histogram to show the color distribution of the Skittles.
  1. Create a histogram to show the color distribution of the M&M’s.
  1. Create a histogram showing the combined color distribution of Skittles and M&Ms.
  1. Create a scatterplot or bar graph to show the distribution of colors for the Skittles.
  1. Create a scatterplot or bar graph to show the distribution of colors for the M&Ms.
  1. Create a scatterplot or bar graph to show the combined color distribution of Skittles and M&Ms.
  1. Create a pie chart to show the distribution of colors of Skittles. Your pie chart MUST include the actual number AND the PERCENTAGES for each color.
  1. Create a pie chart to show the distribution of colors of M&M’s. Your pie chart MUST include the actual number AND the PERCENTAGES for each color.
  1. Create a pie chart to show the combined distribution of color for M&M’s. It must include the actual number AND the PERCENTAGES for each color.

PART 3 Probability and Odds Calculations

In a nutshell, probability and odds are ways of examining the likelihood of an event happening.

Probability can be described as the ratio of a desired outcome to the total possible outcomes.

For example:

If I roll a 6 sided die, the probability of rolling a 2 could be represented as the ratio 1/6. There are 6 possible outcomes but only one 2. So you have a one in 6 chance of rolling a 2. As a decimal this would be .166666666 repeating. As a percentage this would be a 16.7% probability. I find the percentage by dividing the ratio and moving my decimal two places to the right (or multiply by 100). So for this example I have about a 17% chance of rolling a 2.

If I roll a 6 sided die and want to know the probability rolling a 2 OR a 4, the probability could be represented as the ratio 2/6 or a simplified 1/3. As a decimal this would be .333333333 repeating. As a percentage I have a 33.3% probability.

If I roll a 6 sided die TWICE and want to know the probability of rolling a 2 two times in a row, then I have to consider the individual probabilities and multiply them. I have a 1/6 probability the first time, and then a 1/6 probability the second time. Mathematically this looks like:

1/6 X 1/6 = 1/36

So I would have a 1/36 probability of rolling the same number back-to-back times. As a decimal this would be .0277777777 repeating, or a percentage of 2.8%.

Odds can be described as the comparison of desired outcomes to the undesired outcomes.

If I roll a 6 sided die, the odds of rolling a 2 could be represented as 1:5. This basically says that out of 6 possible outcomes 1 is what I want and 5 is not what I want.

If I roll a 6 sided die and want to know the odds of rolling a 2 or 4, the odds could be represented as 2:4 or a simplified 1:2. This says that out of the 6 possible outcomes 2 is what I want and 4 is not what I want. Simplified it says that if I roll the dice three times 1 time will be a 2 or a 4 and the other two times will likely be something other than a 2 or a 4.

Use your Skittles data to complete the Probability and Odds tables below

Probability
Ratio / Decimal / Percentage
Red
Orange
Yellow
Green
Blue
Purple
Brown
Total
Odds (:)
Red
Orange
Yellow
Green
Blue
Purple
Brown

Use your M&M data to complete the Probability and Odds tables below

Probability
Ratio / Decimal / Percentage
Red
Orange
Yellow
Green
Blue
Purple
Brown
Total
Odds (:)
Red
Orange
Yellow
Green
Blue
Purple
Brown

Combine your Skittles and M&Ms together and complete the Probability and Odds tables below

Probability
M&M’s / Skittles / Skittles and M&Ms
Ratio / Decimal / % / Ratio / Decimal / % / Ratio / Decimal / %
Red
Orange
Yellow
Green
Blue
Purple
Brown
M&M
Skittle
Odds (:)
M&M’s / Skittles / Skittles and M&M’s Combined
Red
Orange
Yellow
Green
Blue
Purple
Brown
M&M
Skittle

Part 4 Analysis and Calculation

Mix your Skittles and M&Ms together in your cup. Use and interpret your data from above to answer the following questions:

  1. If a bag of Skittles and a bag of M&M’s cost the same amount of money, which candydo you think is the best deal? Explain your reasoning.
  2. Which color of M&M, if any, do you think is the most common? Explain your reasoning.
  3. Which color of Skittles, if any, do you think is the most common? Explain your reasoning.
  4. What kind and color of candy do you think that you would pull out if you were asked to pull one piece out of your cup blindfolded?
  5. Determine the probability of drawing an orange OR a red candy from your cup. Show your ratio, decimal, and percentage.
  6. Determine the probability of drawing an orange OR a red SKITTLE from your cup. Show your ratio, decimal, and percentage.
  7. Determine the probability (ratio, decimal, and percent) of drawing two red candies in a row. Show your calculations and explain your work. (Put the candy you pulled out back into the cup before drawing again)
  8. Determine the probability (ratio, decimal, and percent) of drawing two Skittles in a row. Show your calculations and explain your work. (Put the candy you pulled out back in the cup before drawing again)
  9. Determine the probability (decimal, ratio, and percent) of drawing two red candies in a row but this time do NOT put the candy back in before drawing the 2nd time. Show your calculations and explain your work. Be sure to explain why your answer is different from your answer to question 7.
  10. Determine the probability (decimal, ratio, and percent) of drawing two Skittles in a row but this time do NOT put the candy back in before drawing the 2nd time. Show your calculations and explain your work. Be sure to explain why your answer is different from your answer to question 8.

Part 5 Proportional Reasoning

Choose one type of candy Skittles or M&M’s and use your population sample (the candy in your bag) to complete the following tasks:

Complete the input output table below to compare red to green for 6 bags of your candy

Red (R) X / Green (G) Y
  1. Right a ratio comparing the number of red to the number of green.
  2. What is the unit rate/slope/rate of change for your table?
  3. Fill in the blank: For every one red piece of candy I have ______green pieces of candy.
  4. Draw a linear graph comparing red candy to green candy. Be sure to label each axis and title your graph.
  5. Write an equation to represent your red to green situation.
  6. If you had 100 red pieces of candy how many green pieces of candy would you have?
  7. If you had 100 green pieces of candy how many red pieces of candy would you have?