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Probability

Probability. What is probability?. In your own words… Probability of an event is the number from 0 to 1 that indicates the likelihood the event will occur. An event is an outcome or collection of outcomes Probabilities can be written as a decimal, a percent, or a fraction.

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Probability

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  1. Probability

  2. What is probability? • In your own words… • Probability of an event is the number from 0 to 1 that indicates the likelihood the event will occur. • An event is an outcome or collection of outcomes • Probabilities can be written as a decimal, a percent, or a fraction.

  3. What is probability? • For example, when rolling a dice there are six possible outcomes or events: 1, 2, 3, 4, 5, or 6. • A different event could be “rolling an odd number”. So, the event would be 1, 3, or 5

  4. Probability • Using a number line can help describe the probability of an event. Event is more likely not to occur Event is more likely to occur P = 1 Event is certain to occur P = 0 Event will not occur P = .5 Even is equally likely to occur or not occur

  5. Theoretical Probability • When all outcomes are equally likely, the theoretical probability that an event A will occur is: • P(A) = number of outcomes in event A ÷ Total number of outcomes • The theoretical probability of an even tis often simply called the probability of the event.

  6. Find Probabilities of an Event • You roll a standard six-sided die. Find to probability of: • Rolling a 5 • Rolling an even number

  7. Find Probabilities of an Event • There are 6 possible outcomes. Only 1 outcome corresponds to rolling a 5. P(rolling a 5) = = # of ways to roll a 5 # of ways to roll the die

  8. Find Probabilities of an Event • Find the probability of rolling an even number. • A total of 3 outcomes correspond to rolling an even number: a 2, 4, or 6 P(rolling even number) = = # of ways to roll an even number # of ways to roll the die

  9. Find Probabilities of an Event • You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event. • A perfect square is chosen. • A factor of 30 is chosen.

  10. Answers • A perfect square is chosen • A factor of 30 is chosen

  11. Use Permutations or Combinations • A community center hosts a talent contest for local musicians. On a given evening, 7 musicians are scheduled to perform. The order in which the musicians perform is randomly selected during the show.

  12. Use Permutations or Combinations • What is the probability that the musicians perform in alphabetical order by their last names? (Assume that no two musicians have the same last name)

  13. Use Permutations or Combinations • There are 7! different permutations of the 7 musicians. Of these, only 1 is in the alphabetical order by last name. • So the probability of is: P(alphabetical order) =

  14. Use Permutation or Combinations • You are friends with 4 of the musicians. What is the probability that the first 2 performers are your friends?

  15. Use Permutations and Combinations • There are 7C2 different combinations of 2 musicians. Of these, 4C2 are 2 of your friends. • So, the probability is: P(first 2 performers are your friends) =

  16. Odds • You can also use odds to measure the likelihood that an event will occur. • Odds measure the chances in favor of an event occurring or the chances against an event occurring.

  17. Odds • When all outcomes are equally likely, the odds in favor and not in favor of an event A are as follows: Odds in favor of event A = Odds not in favor of event A = • You can write the odds in favor of or against an event in the form or in the form a:b. # of outcomes in A # of outcomes not in A # of outcomes not in A # of outcomes in A

  18. Find odds • A card is drawn from a standard deck of 52 cards. Find: • The odds in favor of drawing a 10 • The odds against drawing a club

  19. Find odds • Odds in favor of drawing a 10 = = or 1:12 • Odds against drawing a club = = or 3:1 # of non-clubs # of tens # of non-tens # of clubs

  20. Find Odds • What are the odds: • In favor of drawing a heart • Against drawing a queen

  21. Experimental Probability • Sometimes it is not possible or convenient to find the theoretical probability of an event. • In such cases, you may be able to calculate an experimental probability by performing an experiment, conducting a survey, or looking at the history of the event.

  22. Experimental Probability • When an experiment is performed that consists of a certain number of trials, the experimental probability of an event A is given by: P(A) = # of trials where A occurs Total # of trials

  23. Geometric Probability • Some probabilities are found by calculating a ratio of two lengths, areas, or volumes. • These are called geometric probabilities

  24. Geometric Probability • Length • Area • Volume area of smaller object volume of smaller space length of smaller segment total length total area total volume

  25. Geometric Probability • Darts and Bulls-eye

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