Individual Posts: M&M
Professors Judy Williams and
Mario Scribner, Math 240 (Statistics),
Community College, reproduced by D.
Reiss with permission
- Step 1: Buy a King Size 3.14 oz or larger package of Plain
Step 2: Share the information from the M&M count you did
in Step 1. Respond by 11:59 p.m. Wednesday, since this is information
you already have. Then return for Step 3 instructions.
- Create a Bar plot below for the distribution of colors.
- Count the number of each color and find the modal color.
- Calculate the percentage of each color in a package by taking the
number of each color and dividing by the total number of M&Ms
in a package.
- Record these percentages above the appropriate color on your bar
- Using the relative frequency approach estimate the probability of
selecting a blue M&M.
Reply to this message. Change the Topic line to read:
Total=___ Blue=___ Percent blue=___
where Total is the total number of candies in your bag, Blue is the
number of blue candies in your bag, and Percent blue is -- do I need
to say this? -- your blue/your total (100)
- Step 3: Find the total m&m candies counted by the
class and the total blue candies counted. By the way, M&M/Mars
Company states that M&Ms contain 10% blue candies.
- Calculate the percent blue m&m candies for the class.
- Compare the class percent with your percent.
- How does this exercise illustrate the Law of Large Numbers
Selected Student Responses
Total = 104, Blue = 11, Percent Blue = 10.6%
Total=106 Blue=7 Percent blue=6.6%
Total=286 Blue=36 Percent Blue= 12.58
Total=100, Blue=12 Percent Blue=12% I just wanted to say: no, I did
not eat any M&M's until I was done counting, ha-ha! I actually got
exactly 100 Plain M&M's. My money's worth was missing a few more,
hee-hee! :) Take care all!
Total=106, Blue=20, %Blue= 18.9%
Total=107 Blue=8 Percent=7.5
Total= 101, Blue= 18, % Blue= 17.8% I kind of feel short changed
a few M & M's. I also feel fat thinking that I can eat 101 M &
M's in less than 5 minutes!
Total M&M's for the class = 2602
Total Blue M&M's = 303
Percent Blue = 11.6%
My was slightly higher but very close. (12.58%)
The percentage of blue in a small sample (my bag) is about equal to
the percentage of blue in a large population.
1. There are 2702 total pieces of M&M's.
2. The are 11.5% Blue (312) Blue M&M's
3. The class results vary so drastic, I cannot accurately judge. However,
compared to the majority, it looks comparatively similar.
4. The experiment compares to the Law of Large Numbers because after
the experiment was repeated over and over, the numbers start to average
out to become closer to the stated, or observed, outcome.
1. total m&ms (class) = 2598
total blue (class) = 309
2. percent blue (class) = 11.89%
3. my percent: 20/103 = 19.4%
My percentage doesn't jive very well with the rest of the class. I
must have gotten and outlier bag, but if averaged w/ John's bag, it approaches
the class average. (Sorry, John, I guess I got your blue ones). The
more observations you take, the closer you'll get to the actual average.
Total M&Ms = 2702
Total Blue M&Ms = 312
% Blue M&Ms = 11.55%
I had over the percentage in my bag (18.9%), but I can see how the law
of large numbers applies. The more M&Ms we counted (larger the sample),
the closer we got to the actual probability obtained by relative frequency,
which the company stated was approximately 10%.
Total M&M's for the class = 2705
Total Blue M&M's = 327
Percent Blue M&M's = 12.09%
My percentage of Blue M&M's = 10.58%
Since the individual experiments ranged from 2.88% to 20%, and the class
average is 12.09%, we, collectively, approached the theoretical probability
of 10% which illustrates the Law of Large Numbers.
I have never seen so many different counts and mine is different as well.
I had to subtract 104 M&M's as John's was posted twice. This
is my count.
1. There were 2,598 M&M's counted by the class.
2. Of the 2,598 M&M's, 281 were blue.
3. The class percentage of blue M&M's is 10.8%.
4. This computes to a percentage of 10.8% which is fairly close to the
10% quoted by M&M Company.
5.These calculations come fairly close to the theoretical probability,
which would support the "Law of Large Numbers."