how is it associated with trials of bernoulli?
With regard to its application in probability theory, it is an example of a Bernoulli trial process.
E (mathematical constant)
The number itself also has applications in probability theory, in a way that is not obviously related to exponential growth. Suppose that a gambler plays a slot machine that pays out with a probability of one in and plays it times. Then, for large , the probability that the gambler will lose every bet is approximately . For , this is already approximately 1/2.79.

This is an example of a Bernoulli trial process. Each time the gambler plays the slots, there is a one in "n" chance of winning. Playing "n" times is modeled by the binomial distribution, which is closely related to the binomial theorem and Pascal's triangle.
where is e used in the real world Apart from its presence in the alphabetic order, it is a mathematical constant approximately equal to 2.71828
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E (mathematical constant) [SEP] Bernoulli trials
The number itself also has applications in probability theory, in a way that is not obviously related to exponential growth. Suppose that a gambler plays a slot machine that pays out with a probability of one in and plays it times. Then, for large , the probability that the gambler will lose every bet is approximately . For , this is already approximately 1/2.79. This is an example of a Bernoulli trial process. Each time the gambler plays the slots, there is a one in "n" chance of winning. Playing "n" times is modeled by the binomial distribution, which is closely related to the binomial theorem and Pascal's triangle.