![]() ![]() Given a probability A, denoted by P(A), it is simple to calculate the complement, or the probability that the event described by P(A) does not occur, P(A'). The calculator provided computes the probability that an event A or B does not occur, the probability A and/or B occur when they are not mutually exclusive, the probability that both event A and B occur, and the probability that either event A or event B occurs, but not both. This is further affected by whether the events being studied are independent, mutually exclusive, or conditional, among other things. In its most general case, probability can be defined numerically as the number of desired outcomes divided by the total number of outcomes. It follows that the higher the probability of an event, the more certain it is that the event will occur. It is quantified as a number between 0 and 1, with 1 signifying certainty, and 0 signifying that the event cannot occur. Probability is the measure of the likelihood of an event occurring. Related Standard Deviation Calculator | Sample Size Calculator | Statistics Calculator Use the calculator below to find the area P shown in the normal distribution, as well as the confidence intervals for a range of confidence levels. Probability of a Series of Independent Events Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the The probability of drawing a student's name changes for each of the trials and, therefore, violates the condition of independence. ![]() ![]() The probability is 6 15 6 15, when the first draw selects a staff member. The probability of a student on the second draw is 5 15 5 15, when the first draw selects a student. The probability of a student on the first draw is 6 16 6 16. However, the trials are not independent because the outcome of the first trial affects the outcome of the second trial. The first name drawn determines the chairperson and the second name the recorder. What is the probability that the chairperson and recorder are both students? The names of all committee members are put into a box, and two names are drawn without replacement. The committee wishes to choose a chairperson and a recorder. ABC College has a student advisory committee made up of ten staff members and six students. It violates the condition of independence. The following example illustrates a problem that is not binomial. A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials. The standard deviation, σ, is then σ = n p q n p q.Īny experiment that has characteristics two and three and where n = 1 is called a Bernoulli Trial (named after Jacob Bernoulli who, in the late 1600s, studied them extensively). The mean, μ, and variance, σ 2, for the binomial probability distribution are μ = np and σ 2 = npq. The random variable X = the number of successes obtained in the n independent trials. The outcomes of a binomial experiment fit a binomial probability distribution. This means that for every true-false statistics question Joe answers, his probability of success ( p = 0.6) and his probability of failure ( q = 0.4) remain the same. Suppose Joe always guesses correctly on any statistics true-false question with probability p = 0.6. ![]() If a success is guessing correctly, then a failure is guessing incorrectly. For example, randomly guessing at a true-false statistics question has only two outcomes. Another way of saying this is that for each individual trial, the probability, p, of a success and probability, q, of a failure remain the same. Because the n trials are independent, the outcome of one trial does not help in predicting the outcome of another trial. The n trials are independent and are repeated using identical conditions.The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial. There are only two possible outcomes, called "success" and "failure," for each trial.The letter n denotes the number of trials. Think of trials as repetitions of an experiment. There are three characteristics of a binomial experiment. ![]()
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