Bernoulli scheme, binomial distribution, eco-friendly behavior, probability calculation, survey analysis, statistical probability, eco-responsible behavior, random sampling
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This document discusses the probability of people adopting eco-friendly behavior based on a survey, using a Bernoulli scheme and binomial distribution.
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[...] It is therefore a Bernoulli trial with a probability of 0.54. In asking 12 people randomly and independently and counting the number of we therefore construct a Bernoulli scheme of 12 trials with a probability of 0.54 of success. The random variable Y therefore follows a binomial distribution with parameters 12 and 0.54. The probability of having The number of people out of the 12 adopting an eco-friendly behavior is then given by: One notices that: This calculation therefore allows us to calculate the probability of exactly 3 people adopting an eco-responsible behavior among the 12 people interviewed. [...]
[...] b./ So we want to calculate . We notice that the opposite event is: 'none of the 12 people interviewed adopt an eco-responsible behavior'. This event corresponds to the probability . So we have: The probability of having at least one person among those interviewed adopting an eco-responsible behavior is therefore 0.999984 or 99.9984%. c./ So we are looking to calculate . We have: The probability of having at least half of the respondents adopting an eco-responsible behavior is therefore 0.6062 or 60.26%. [...]
