Probability

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Probability

  1. 1. Probability Vocabulary Random Phenomenon Sample space Outcome Trial Event Probability Probability model Complement Independent Mutually exclusive Conditional probability Combination permutation
  2. 2. 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)
  3. 3. 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.
  4. 4. 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
  5. 5. 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
  6. 6. 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
  7. 7. 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)
  8. 8. 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
  9. 9. Rules of Probability- Addition
  10. 10. Rules of Probability-Multiplication
  11. 11. Conditional ProbabilityConditional probability describes the situation wherethe probability of a second event is dependent upon a first event having occurred
  12. 12. 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
  13. 13. Possible outcomes and countingtechniques
  14. 14. Possible outcomes and countingtechniques
  15. 15. Review Questions
  16. 16. Review Questions
  17. 17. Review Questions
  18. 18. Review Questions
  19. 19. Review Questions
  20. 20. Review Questions

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