The prediction for the number of passwords in which the first character is a vowel is 56 passwords.
<h3>How to find that a given condition can be modelled by binomial distribution?</h3>Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
The probability that out of n trials, there'd be x successes is given by
The expected value and variance of X are:
Given that the characters that can be used are numbers 0 through 9 and lowercase letters. Therefore, a total of 36 different characters are available.
Since we need to know the passwords made with vowels, therefore, the probability of a password in which the first character will be a, e, i, o, u is (5/36).
Now as the computer produces 400 passwords, therefore, the predicted value can be written as,
Hence, the prediction for the number of passwords in which the first character is a vowel is 56 passwords.
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