![]() ![]() If our classroom size is 20 and our trials were independent (e.g. Let’s say we’re interested in understanding the probability that all 4 randomly selected students prefer football over basketball. Let random variable X be the number of students randomly selected in 4 trials who prefer football over basketball. S uppose the true proportion of students in a certain class who prefer football over basketball is 50%. To develop an intuition behind The 10% Condition, consider the following example. The 10% Condition: As long as the sample size is less than or equal to 10% of the population size, we can still make the assumption that Bernoulli trials are independent. In cases where the trials are not actually independent, we can still assume that they are if the sample size we’re working with does not exceed 10% of the population size. However, in order to do so we must assume that the trials are independent. Often in statistics when we want to calculate probabilities involving more than just a few Bernoulli trials, we use the normal distribution as an approximation. ![]() ![]() The coin can only land on two sides (we could call heads a “success” and tails a “failure”) and the probability of success on each flip is 0.5, assuming the coin is fair. A Bernoulli trial is an experiment with only two possible outcomes – “success” or “failure” – and the probability of success is the same each time the experiment is conducted.Īn example of a Bernoulli trial is a coin flip. ![]()
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