# Mutually Exclusive and Compound Events

Consider a standard deck of cards. Fill in the blanks to make the statements true.

1. P(_______) = P(_____) OR P(_____)
2. P(_______) = P(_____) AND P(_____)
3. P(NOT_______) = P(_____) OR P(NOT_____)
4. P(NOT_______) = P(_____) AND P(NOT_____)

How many different true statements can you make?

Using the following templates, draw a diagram for each statement you make.

# Data and Standard Deviation2- Open Middle Problem

So my local Probability and Statistics guru (@veganmathbeagle) sent me a problem she encountered in a textbook that was very Open Middle-ish.  I modified it a bit and here it is…

Directions: Using the numbers 1 to 9, using each only once, create a data set of 4 numbers that fit the following criteria:

The four numbers have the smallest possible standard deviation:

___ , ___ , ___ , ___

The four numbers have the largest possible standard deviation:

___ , ___ , ___ , ___

1. Is there more than one data set for either question?  If so, what is it?
2. How would allowing the use of repeat numbers effect the standard deviation?
3. What would your data sets look like if this was allowed?

# Data and Standard Deviation- Open Middle Problem

Directions: Using the numbers 1 to 9, using each only once, create a data set of 5 numbers that fit the following criteria:

Mean = 5

Standard Deviation = 2.6

___ , ___ , ___ , ___ , ___

1. Create a data set with the same mean but a smaller standard deviation
2. Create a data set with the same mean but a larger standard deviation
3. Explain why your standard deviation changes but your mean remains the same
4. Explain what changes would happen if this is a sample of the population
5. What would happen to your mean and standard deviation if you added 20 to each of your initial data points?

# Correlations- Open Middle Problem

Directions: Using the numbers 0-9, without repetition for each case, create a set of points that have the following characteristics:

Non-linear Positive Correlation

(__,__) (__,__) (__,__) (__,__) (__,__)

Non-linear Negative Correlation

(__,__) (__,__) (__,__) (__,__) (__,__)

No Correlation

(__,__) (__,__) (__,__) (__,__) (__,__)