1099 11.7 Basics of Probability 11.7 Basics of Probability ■ Basic Concepts ■ Complements and Venn Diagrams ■ Odds ■ Compound Events ■ Binomial Probability Any subset of a sample space is an event. In the experiment with the die, for example, “the number showing is a 3” is an event, say E1, such that E1 = 536. “The number showing is greater than 3” is also an event, say E2, such that E2 = 54, 5, 66. To represent the number of outcomes that belong to event E, the notation n1E2 is used. Then n1E12 = 1 and n1E22 = 3. The notation P1E2 is used for the probability of an event E. If the outcomes in the sample space for an experiment are equally likely, then the probability of event E occurring is found as follows. Probability of Event E In a sample space with equally likely outcomes, the probability of event E, written P1E2 , is the ratio of the number of outcomes in sample space S that belong to event E, n1E2, to the total number of outcomes in sample space S, n1S2. P1E2 = n1E2 n1S2 To find the probability of event E1 in the die experiment, start with the sample space, S = 51, 2, 3, 4, 5, 66, and the desired event, E1 = 536. P1E12 = n1E12 n1S2 = 1 6 Use n1E12 = 1 and n1S2 = 6. Experiment Sample Space Toss a coin. S = 5H, T6 Roll a die. S = 51, 2, 3, 4, 5, 66 Toss two coins. S = 51H, H2, 1H, T2, 1T, H2, 1T, T26 Answer a true/false question. S = 5true, false6 Use set notation for a sample space. Basic Concepts In probability, each repetition of an experiment is a trial. The possible results of each trial are outcomes of the experiment. In this section, we are concerned with outcomes that are equally likely to occur. (We assume that a die has 6 faces and a coin has 2 sides.) For example, the experiment of tossing a fair coin has two equally likely outcomes: landing heads up 1H2 or landing tails up 1T2. Also, the experiment of rolling a fair die has 6 equally likely outcomes: landing so the face that is up shows 1, 2, 3, 4, 5, or 6 dots. The set S of all possible outcomes of a given experiment is the sample space for the experiment. (In this section, all sample spaces are finite.) A sample space S can be written in set notation.
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