May 28th, 2015
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ProbabilityExample 1: Simple ProbabilityYou roll a six-sided die whose sides are numbered from 1 through 6. Find: (a) P(4) (b) P(rolling an odd number)(c) P(rolling a number less than 5)(d) P(rolling a 1 or a 4)(e) P(rolling a 1, 2, 3, 4, 5, or 6)(f) P(not 4)(g) P(7) We learned a few of the very basic rules of probability in Example 1: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 outcomesThe probability of an event occurring is between 0 and 1, inclusive.The sum of the probabilities for all possible outcomes is equal to 1.The probability that an event does not occur is 1 minus the probability that the event does occur: P(A') = 1 - P(A). Another way of saying this is that the probability of an event and its complement sum to 1: P(A) + P(A') = 1Here are a few other basic probability rules that we will study in the examples that follow:If A and B are two events, then P(A or B) = P(A) + P(B) - P(A and B).If A and B are independent events, then P(A and B) = P(A)P(B).If A and B are dependent events, then P(A and B) = P(A)P(B|A).Discrete Random VariableDef: A discrete random variable is the result of a count or statistical experiment that can take a countable, finite number of values Examples: number of students in a class, bikes in the parking lot, outcomes of rolling a die, number of sisters you haveWhy are the foll

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