11/13 Basic probability Probability in our context has to do with the outcomes of repeatable experiments Need an Experiment Set X of outcomes (outcome.

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Presentation transcript:

11/13 Basic probability Probability in our context has to do with the outcomes of repeatable experiments Need an Experiment Set X of outcomes (outcome space) from the experiment: They should be disjoint (mutually exclusive) and exhaustive (include all possible outcomes) Events are sets of outcomes (subsets of the outcome space). We want to be able to assign a probability that an event E will occur when the experiment is repeated.

Example: A pair of dice are rolled. What is the outcome space? Let E be the event ‘a 7 is rolled’ Let F be the event ‘an 11 is rolled’ ’

Basic properities of a probability function. Outcomes: S = {x1, x2, x3, … E, F events 1. P(E) >= 0 for any event E. 2. P(S) = 1 3.If E and F are mutually exclusive, then Consequences: 4. 5.

Uniform probability function: Each outcome has the same probability. Define the probability of an event E To be P(E) = n(E)/n(X) where X is the outcome space. The 3 rules of probability hold ( and so all of the consequences hold)

Sampling to discover probabilities Common #14 An experiment consists of studying the hair color of all members of families with one child.

Sampling to discover probabilities Common #6 By sampling, a cell-phone provider discovers That 2% of calls fail to reach the network, another 5% are dropped by the network and an additional 2% fail to reach the callee. What is the probability that random cell call will fail to connect?

Calculating probabilities in games: Lottery. What is the probability of winning Powerball?

Calculating probabilities in games: Poker: What is the probability of getting a flush in a random 5 card hand? What is the probability of getting at least a pair in a random 5 card hand?