Module 1
● Big Ideas from Module 1
○ Steps Necessary to Perform a Simulation
○ Classifying data and variables (quantitative vs qualitative or categorical)
○ Five W’s and an H for data
○ Graphical displays for categorical data
○ Computing and interpreting conditional proportions
○ Interpreting a comparative bar chart
○ Graphical displays for quantitative data
○ Measures of center
○ Measures of spread
○ The Empirical Rule
○ Constructing and interpreting boxplots
○ Determining potential outliers
○ Computing and interpreting z-scores
○ Misleading graphical displays
○ Using SOCS to describe graphical displays
○ Three types of probability (subjective, empirical, experimental)
○ Properties of probability
○ Law of Large Numbers
○ Probability vocabulary (Sample Space, Events, Complement, Disjoint, Intersections,
Unions)
○ Constructing and interpreting tree diagrams and Venn Diagrams
○ Probability formulas and finding probabilities
○ Conditional probability
○ Determining if two events are independent (3 methods)
○ Determining if two events are disjoint (mutually exclusive)
○ Sensitivity and specificity
Specific Sticky Points:
1. Simulation - Many students struggle to correctly identify the component that is to be
repeated. That is the one thing that you are actually simulating through the use of a
random device.
2. In Part 2, we studied ways to summarize data graphically and numerically. We learned
how to select appropriate graphical and numerical summaries based on the type of data
we are working with (i.e. quantitative or qualitative). We also briefly examined
misleading graphical displays. We learned how to describe the distribution of
quantitative data using SOCS.
3. Computing Conditional Proportions – Please make sure you remember that you must
always condition on levels of the explanatory variable. If you always put your
explanatory variables in the rows of the contingency table, you will always be dividing by
the row totals.
, 4. Unions, Intersections, and Complements
● The event (A ∪ B) , read “A union B” or “A or B,” means all outcomes in either
event A, event B, or both.
○ In the context of probability, “or” means one, or the other, or both.
● The event (A ∩ B) , read “A intersection B” or “A and B” means only all
outcomes common to both event A and event B.
○ In the context of probability, “and” means both.
● The event A′ , read “A complement” or “not A,” means all outcomes not in event
A
5. General Addition Rule: Determining P(A or B)
● For any two events A and B, we can find P(A or B) using the general addition
rule. It is important to be able to recognize when it is appropriate to use this rule!
○ General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
6. Determining P(A and B)
● If we are told that two events A and B are independent, we know that P(A and B)
= P(A)*P(B). In other words, all we need to do is multiply the two individual event
probabilities together. This only works if we know that the two events are
independent.
● If we are told that two events A and B are mutually exclusive, we know that P(A
and B) = 0. T he two events cannot possibly happen at the same time.
● If we do not know if the events A and B are independent or mutually exclusive,
we can find P(A and B) by using the general addition rule and working
backwards. We would need to know P(A or B), P(A), and P(B) in order to do
that.
7. Conditional Probability – When solving conditional probability problems, it is best to
use the conditional probability rule. These two versions are equivalent.
P (A and B)
● P(A | B) = P (B )
P (A and B)
● P(B | A) = P (A)
● Notice that the probability of the given event appears in the denominator of this
formula.
8. Methods for Determining Statistical Independence – There are three methods that
can be used to check for statistical independence. If you are asked to determine if 2
events are independent, you must use one of these three methods and show your
work by actually computing probabilities. You only need to use one of them because
they all will give the same result. To show that two events A and B are independent, you
need to show that either:
● P(A and B) = P(A)*P(B)
● P(A | B) = P(A)
● P(B | A) = P(B)
● Big Ideas from Module 1
○ Steps Necessary to Perform a Simulation
○ Classifying data and variables (quantitative vs qualitative or categorical)
○ Five W’s and an H for data
○ Graphical displays for categorical data
○ Computing and interpreting conditional proportions
○ Interpreting a comparative bar chart
○ Graphical displays for quantitative data
○ Measures of center
○ Measures of spread
○ The Empirical Rule
○ Constructing and interpreting boxplots
○ Determining potential outliers
○ Computing and interpreting z-scores
○ Misleading graphical displays
○ Using SOCS to describe graphical displays
○ Three types of probability (subjective, empirical, experimental)
○ Properties of probability
○ Law of Large Numbers
○ Probability vocabulary (Sample Space, Events, Complement, Disjoint, Intersections,
Unions)
○ Constructing and interpreting tree diagrams and Venn Diagrams
○ Probability formulas and finding probabilities
○ Conditional probability
○ Determining if two events are independent (3 methods)
○ Determining if two events are disjoint (mutually exclusive)
○ Sensitivity and specificity
Specific Sticky Points:
1. Simulation - Many students struggle to correctly identify the component that is to be
repeated. That is the one thing that you are actually simulating through the use of a
random device.
2. In Part 2, we studied ways to summarize data graphically and numerically. We learned
how to select appropriate graphical and numerical summaries based on the type of data
we are working with (i.e. quantitative or qualitative). We also briefly examined
misleading graphical displays. We learned how to describe the distribution of
quantitative data using SOCS.
3. Computing Conditional Proportions – Please make sure you remember that you must
always condition on levels of the explanatory variable. If you always put your
explanatory variables in the rows of the contingency table, you will always be dividing by
the row totals.
, 4. Unions, Intersections, and Complements
● The event (A ∪ B) , read “A union B” or “A or B,” means all outcomes in either
event A, event B, or both.
○ In the context of probability, “or” means one, or the other, or both.
● The event (A ∩ B) , read “A intersection B” or “A and B” means only all
outcomes common to both event A and event B.
○ In the context of probability, “and” means both.
● The event A′ , read “A complement” or “not A,” means all outcomes not in event
A
5. General Addition Rule: Determining P(A or B)
● For any two events A and B, we can find P(A or B) using the general addition
rule. It is important to be able to recognize when it is appropriate to use this rule!
○ General Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)
6. Determining P(A and B)
● If we are told that two events A and B are independent, we know that P(A and B)
= P(A)*P(B). In other words, all we need to do is multiply the two individual event
probabilities together. This only works if we know that the two events are
independent.
● If we are told that two events A and B are mutually exclusive, we know that P(A
and B) = 0. T he two events cannot possibly happen at the same time.
● If we do not know if the events A and B are independent or mutually exclusive,
we can find P(A and B) by using the general addition rule and working
backwards. We would need to know P(A or B), P(A), and P(B) in order to do
that.
7. Conditional Probability – When solving conditional probability problems, it is best to
use the conditional probability rule. These two versions are equivalent.
P (A and B)
● P(A | B) = P (B )
P (A and B)
● P(B | A) = P (A)
● Notice that the probability of the given event appears in the denominator of this
formula.
8. Methods for Determining Statistical Independence – There are three methods that
can be used to check for statistical independence. If you are asked to determine if 2
events are independent, you must use one of these three methods and show your
work by actually computing probabilities. You only need to use one of them because
they all will give the same result. To show that two events A and B are independent, you
need to show that either:
● P(A and B) = P(A)*P(B)
● P(A | B) = P(A)
● P(B | A) = P(B)
