UP - Using Probability to Make Decisions Overview

Using Probability to Make Decisions Overview

Introduction

vegasViva Las Vegas! The gambling capital of the world may be able to help you with understanding probability, mathematical fairness, payoffs, and risks! Probability and expected value can be used in every day life situations, such as gambling, driving, investing and fashion! You can calculate endless possibilities from your outfits by using probability to mix and match your favorite pieces! In this unit, you will explore these situations and other decision making situations that involve probability and statistics?

 

Essential Questions

    1. How do we use Venn Diagrams to organize information?
    2. How do we use Tree Diagrams to organize information?  
    3. How do we use Area Models to organize information?  
    4. How many choices do we have to make?  
    5. What role does probability play in games of chance?
    6. How do we mathematically confirm/deny the risk of driving?
    7. What are some everyday decisions we make based on probability?
    8. How is the expected value used to analyze mathematical fairness, payoff, and risk?
    9. Do you receive an allowance? If so, do you deserve more?
    10. How can we use a zero-sum game to analyze real-life situations?

 

Key Terms

The following key terms will help you understand the content in this module.

  • area model - a diagram using fractions to visualize probability
  • binomial probability - the probability of getting one of two outcomes.
  • calculated risk - a risk that is taken after careful consideration of risk probability
  • complement of an event - the opposite of an event, the event does not occur P(A') = 1-P(A)
  • compound events - the probability of two or more things happening at once
  • conditional probability - the probability of Event B given that Event A has already occurred or is certain to occur.
  • dependent events - when events are dependent, the outcome of one event affects the outcome of another event  P(A and B) = P(A) x P(B|A) The symbols P(B|A) denote this process of finding the probability of a dependent event (in this case, Event B). Event B is conditional on Event A having occurred.
  • equally likely - the probability that any event will occur is the same for all events
  • independent events - when events are independent, the outcome of one event does not affect the outcome of another event P (A and B) = P(A) • P(B)
  • mutually exclusive - the probability of two or more things that cannot happen at the same time. P (A or B) = P(A) + P(B) *if two events are not mutually exclusive   P(A or B) = P(A) + P(B)- P(A and B)
  • probability - the likelihood that an outcome will occur
  • sample space - all possible outcomes for the event
  • tree diagram - a diagram used to display stages of compound events
  • Venn diagram - a diagram used to organize data for comparisons

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