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This means that this "unlikely event" has a probability of 63.23% of happening if 1,000 independent trials are conducted. If the number of trials were increased to 10,000, the probability of it happening at least once in 10,000 trials rises to ( 1 − 0.999 10000 ≈ 0.99995, or ) 99.995%. In other words, a highly unlikely event, given enough ...
An example of long division performed without a calculator. A more detailed breakdown of the steps goes as follows: Find the shortest sequence of digits starting from the left end of the dividend, 500, that the divisor 4 goes into at least once. In this case, this is simply the first digit, 5.
For a greater than 50% chance that at least one other person in a roomful of n people has the same birthday as you, n would need to be at least 253. This number is significantly higher than 365 / 2 = 182.5 : the reason is that it is likely that there are some birthday matches among the other people in the room.
Dunbar's number has become of interest in anthropology, evolutionary psychology, [12] statistics, and business management.For example, developers of social software are interested in it, as they need to know the size of social networks their software needs to take into account; and in the modern military, operational psychologists seek such data to support or refute policies related to ...
A continuous function () on the closed interval [,] showing the absolute max (red) and the absolute min (blue).. In calculus, the extreme value theorem states that if a real-valued function is continuous on the closed and bounded interval [,], then must attain a maximum and a minimum, each at least once.
In this example, one tries to increase the probability of a rare event occurring at least once by carrying out more trials. For example, a job seeker might argue, "If I send my résumé to enough places, the law of averages says that someone will eventually hire me."
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Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.