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Complementary events are two events in which either one or the other must happen, but both cannot happen at the same time. The sum of the probabilities of complementary events is 1. Example 2 There is a 25% chance that Sam will win a prize. What is the probability that Sam will not win a prize? P(win) + P(not win) = 1 0.25 + P(not win) = 1

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Consider a community in which the probability one is retired is 0.3333 (33.33%), and the probability someone uses online banking is 0.3800 (38.00%). If the joint probability that a community member selected at random is both retired and uses online banking is 0.0800 (8.00%), we may conclude that the events of being retired and banking online are

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Probability is a measure of how likely an event is to happen. Something that is impossible has a value of zero and something that is certain has a value of one. The range of values from zero to one is called a probability scale. A probability cannot be negative or be greater than one.

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The formula to calculate the probability that an event will occur exactly n times over multiple trials is intricately tied to the formula for combinations. This may be a surprise at first, but upon examination there is a clear connection between combinations and multiple trial probabilities.

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˝If two events A and B are not mutually exclusive, then the probability that at least one of them occurs, is given by the sum of the separate probabilities of events A and B minus the probability of the joint event A ð˙ B. ˛ Example: If one card is selected at random from a deck of 52 playing cards, what is the probability

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The Classical or 'A Priori' Definition of Probability If a random experiment can produce n mutually exclusive and equally likely outcomes, and if m out to these outcomes are considered favourable to the occurrence of a certain event A, then the probability of the event A, denoted by P(A), is defined as the ratio m/n.