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Probability Probability Presentation Transcript

  • Probability Vocabulary Random Phenomenon Sample space Outcome Trial Event Probability Probability model Complement Independent Mutually exclusive Conditional probability Combination permutation
  • Key Points P(A)= (the number of times the desired outcome occurs) ÷ (the total number of trials) Events are independent if the outcome of one event does not influence the outcome of any other event Events are mutually exclusive if they cannot occur together Addition Rule: P(A or B)= P(A) + P(B) – P(A and B) Multiplication Rule: If A and B are independent events, P(A and B)= P(A)P(B)
  • Probability _________ is the branch of math that studies patterns of chance The idea of probability is based on observation. Probability describes what happens over many, many trials. The probability, P(A), of any outcome of a random phenomenon is the proportion of times the outcome would occur in a long series of repetitions.
  • Probability- terms In probability, an experiment is any sort of activity whose results cannot be predicted with certainty The _____ _____, S, is the set of all possible outcomes An _______ is one of the possible results that can occur as a result of an experiment A trial is a single running or observation of a random phenomenon An _____ is any outcome or set of outcomes of a random phenomenon
  • Probability P(A)= (the number of times the desired outcome occurs) ÷ (the total number of trials)Example Ryan rolls the die 20 times and gets a 5 on 7 of the rolls. Then, the probability of rolling a 5 is: P(A)= (the number of times you roll a 5) ÷ (the number of times you roll the die)= 7/20
  • Experimental v TheoreticalProbability When a random phenomenon has k possible outcomes that are all equally likely, then each outcome has the probability 1/k. This is called theoretical probability The actual outcome of an experimental activity is called experimental probability
  • Probability- General Rules 1. Probability is a number between 0 and 1. 2. The sum of the probabilities of all possible outcomes in a sample space is 1. 3. The probability that an event does not occur is 1 minus the probability that it does occur. (also called the complement of A) If an event has the probability of .3 of happening, then it has a probability of .7 of not happening( 1-0.3= 0.7)
  • Independence and MutuallyExclusive Events or trials are said to be _________ if the outcome of an event or trial doesn’t influence the outcome of another event or trial Two events are ______ _______ if they cannot occur together Sam can either pass the test or fail- cant do both at same time
  • Rules of Probability- Addition
  • Rules of Probability-Multiplication
  • Conditional ProbabilityConditional probability describes the situation wherethe probability of a second event is dependent upon a first event having occurred
  • Possible outcomes and countingtechniques If you can do one task in A ways and a second task in B ways, then both tasks can be done in A x B ways. Flip a coin and toss a die (2)(6)= 12 possible outcomes
  • Possible outcomes and countingtechniques
  • Possible outcomes and countingtechniques
  • Review Questions
  • Review Questions
  • Review Questions
  • Review Questions
  • Review Questions
  • Review Questions