# Modeling Binomial & Geometric Distributions Using M&M`s ```Bonus: Modeling Binomial &amp; Geometric Distributions using M&amp;M’s
Do Not Eat Until Complete!
Binomial Distributions:
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Suppose that the BLUE M&amp;M is defective.
As randomly as possible, select a sample of 10 M&amp;Ms and record the number of blue ones.
Replace the M&amp;Ms and repeat 5 more times, keeping track of the number of blue M&amp;Ms.
Put your results in a table.
1) Does the observed distribution seem to follow the hypothesized binomial distribution determined by the
binomial n = 10 and p = .24 (according to the company, probability of blue = .24)?
2) How do the mean and standard deviation of your sample distribution compare to   np and
  np1  p  for the theoretical distribution?
Geometric Distribution:
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Suppose that the RED M&amp;M is defective.
As randomly as possible, draw one M&amp;M out at a time.
Continue to draw out M&amp;Ms until you get a red one.
Record X = the number of M&amp;Ms required to draw the first red.
Replace the M&amp;Ms and repeat 5 more times, recording X.
Put your results in a table.
3) Does the observed distribution seem to follow the hypothesized geometric distribution determined by the
p = .13 (according to the company, probability of red = .13)?
4) How do the mean and standard deviation of the class distribution compare to  
the theoretical distribution?
Now you can eat! Enjoy!
1 p
1
and  
for
p
p2
```