Soccer Penalty Kicks - All Things Probability


Ch. 14 & 15: Probability Rules

14.1: Be able to state, explain, understand, and explain the Law of Large Numbers
  1. Know that the relative frequency of an outcome of random phenomenon settles down as we gather more random outcomes.
  2. Understand that random phenomena are unpredictable in the short term but show long-run regularity
  3. Be able to recognize random outcomes in a real-world situation
  4. Be able to use statements about probability in describing random phenomenon
14.2: Know the basic definitions and rules of probability
  1. Recognize when events are disjoint and when events are independent. Understand the difference, and that disjoint events cannot be independent.
  2. Be able to use facts about probability to determine whether an assignment of probabilities is legitimate. Each probability must be a number between 0 and 1, and the sum of all probabilities assigned to all possible outcomes must be 1.
  3. Know how to use the Complement Rule to make calculating probabilities simpler
  4. Know and be able to correctly use the terms "sample space", "disjoint events", and "independent events"
14.3: Know how and when to apply the Addition Rule/General Addition Rule
  1. Know how to apply the Addition Rule for disjoint events
  2. Know how to apply the Addition Rule for non-disjoint events
14.4: Know how and when to apply the Multiplication Rule
  1. Know how to apply the Multiplication Rule for independent events
  2. Know how to apply the Multiplication Rule for non-independent events
14.5: Understand the concept of conditional probability as redefining the Who of concern, according to the information about the event that is given
  1. Know how to make and use a tree diagram to understand conditional probabilities and reverse conditioning
  2. Be able to make a clear statement about a conditional probability that makes clear how the condition affects the probability
14.6: Understand the concept of independence
  1. Be able to make a statement supporting the independence of two events
  2. Avoid making statements that assume independence of events when there is no clear evidence that they are in fact independent


Ch. 16: Random Variables

16.1: Be able to find the probability model for a random variable
  1. Be able to recognize random variables
  2. Know that an assignment of probabilities is legitimate
16.2: Know how to find the mean(expected value) and the variance of a random variable
  1. Always use proper notation for these population parameters, (mu) or E(X) for the mean, and (sigma), SD(X), (sigma-squared), or Var(X) when discussing variability
  2. Be able to interpret the meaning of the expected value and standard deviation of a random variable in the proper context
16.3: Know how to determine the new mean and standard deviation after adding a constant or multiplying by a constant
16.4: Know how to determine the new mean and standard deviation after adding/subtracting two(or more) independent random variables
  1. Understand that variables must be independent in order to determine the variability of their sum or difference by adding variances

Ch. 17: Probability Models

17.1: Be able to choose whether to use a Geometric or Binomial model for a random variable involving Bernoulli trials
  1. Know how to tell if a situation involves Bernoulli Trials
17.2: Know how to use the Geometric model
  1. Know how to find expected value of a Geometric model
  2. Know how to calculate Geometric probabilities
  3. Know the appropriate conditions for using a Geometric model
  4. Be able to interpret means, standard deviations, and probabilities in the Bernoulli trial context
17.3: Know how to use the Binomial model
  1. Know how to find the mean and standard deviation of a Binomial model
  2. Be able to calculate Binomial probabilities, perhaps estimating with a normal model
  3. Be able to interpret means, standard deviations, and probabilities in the Bernoulli trial context