(10:00am EST) Intro to Probability
SAT Score Range
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7 sessions
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AP
CM
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About
About
A little bit about me! I just graduated high school and I'm excited to offer this short course in statistics. I scored a 5 on the AP Statistics exam last year and I also have experience in Discrete Mathematics.
This summer course offers a mathematically rigorous yet accessible introduction to probability.
Students will explore:
- Basic probability and sample spaces
- Simulations and the Law of Large Numbers
- Compound and conditional probability
- Bayes' Theorem
- Discrete probability distributions, including binomial models
The course consists of six main sessions, each one hour long, having a clear, structured lecture followed by guided example problems. A seventh and final session will offer a comprehensive review and a set of cumulative problems to reinforce learning and retention. After each session, lecture notes as well as optional review materials will be provided to help students revisit key ideas at their own pace.
Ideal for students preparing for AP Statistics, Discrete Mathematics, or anyone curious about the subject of probability.
Tutored by
✋ ATTENDANCE POLICY
If you need to miss a session, no problem! Just let me know in advance or as soon as you’re able. Recordings, notes, and review materials will be provided so you can stay caught up at your own pace. My goal is to support your learning, so don’t hesitate to reach out if you need help catching up or reviewing content.
SESSION 1
10
Jun
SESSION 1
Orientation
Orientation
Tue 2:00 PM - 3:00 PM UTCJun 10, 2:00 PM - 3:00 PM UTC
Sample Spaces, Probability, and the Law of Large Numbers
Introduce the basic terminology and structure of probability theory. Define outcomes, sample spaces, and events using formal set notation. Look at the classical (theoretical) and experimental (empirical) definitions of probability. Introduce the Law of Large Numbers and establish reasoning about randomness, uncertainty, and fairness.
Topics covered:
- Set Notation
- Sample Spaces and Events
- Classical and Empirical probability
- Law of Large Numbers
SESSION 2
12
Jun
SESSION 2
AP Statistics
AP Statistics
Thu 2:00 PM - 3:00 PM UTCJun 12, 2:00 PM - 3:00 PM UTC
Compound Events, Venn Diagrams, and the Addition Rule
Develop a formal understanding of compound events. Differentiate between mutually exclusive and non-mutually exclusive events. Establish the Addition Rule and use Venn diagrams and set operations to compute probabilities for unions of events.
Topics covered:
- Mutually and non-mutually exclusive events
- Addition Rule
- Venn diagrams
SESSION 3
17
Jun
SESSION 3
AP Statistics
AP Statistics
Tue 2:00 PM - 3:00 PM UTCJun 17, 2:00 PM - 3:00 PM UTC
Dependence, Joint Probabilities, and the Multiplication Rule
Define independence and dependence in probability. Introduce the Multiplication Rule to compute the joint probability of multiple events. Distinguish joint and conditional probabilities and apply the rule in structured and contextual scenarios.
Topics covered:
- Independent and dependent events
- Multiplication Rule
- Joint probability
- Conditional probability
SESSION 4
19
Jun
SESSION 4
AP Statistics
AP Statistics
Thu 2:00 PM - 3:00 PM UTCJun 19, 2:00 PM - 3:00 PM UTC
Conditional Probability and Tree Diagrams
Formalize the concept of conditional probability and present its standard formula. Demonstrate the use of tree diagrams to compute probabilities in multistage processes. Identify dependent events through probability computations.
Topics covered:
- Conditional probability
- Tree diagrams
- Sequential events
SESSION 5
24
Jun
SESSION 5
AP Statistics
AP Statistics
Tue 2:00 PM - 3:00 PM UTCJun 24, 2:00 PM - 3:00 PM UTC
Bayes’ Theorem, Inverse probabilities, and the Law of Total Probability
Present Bayes’ Theorem as a tool for computing inverse probabilities. Derive its formula using the Law of Total Probability and apply it to problems.
Topics covered:
- Bayes’ Theorem
- Inverse probabilities
- Law of Total Probability
SESSION 6
26
Jun
SESSION 6
AP Statistics
AP Statistics
Thu 2:00 PM - 3:00 PM UTCJun 26, 2:00 PM - 3:00 PM UTC
Overview of Probability Distributions
Define discrete probability distributions and conditions for validity. Construct and interpret uniform distributions. Introduce the concepts of expected value and standard deviation. Look at the binomial distribution and its parameters.
Topics covered:
- Discrete distributions
- Uniform distribution
- Expected value and Standard deviation
- Binomial distribution and Binomial formula
SESSION 7
1
Jul
SESSION 7
Review
Review
Tue 2:00 PM - 3:00 PM UTCJul 1, 2:00 PM - 3:00 PM UTC
Cumulative Review and Final Assessment
Review Topics:
- Compound probability
- Conditional reasoning
- Probability distributions