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.

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

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 = 0 Event will not occur P = .5 Even is equally likely to occur or not occur P = 1 Event is certain to occur

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.

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

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

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

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.

Answers A perfect square is chosen A factor of 30 is chosen

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.

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)

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) =

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

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) =

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.

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

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

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

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

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.

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

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

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

Geometric Probability Darts and Bulls-eye