Respuesta :
The probability that the experiment results in exactly successes is; [tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
How to find that a given condition can be modeled by binomial distribution?
Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Consider that we have random variable X about binomial distribution with parameters n and p, then it can be written as;
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there be x successes is given as;
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are given as:
[tex]E(X) = np\\Var(X) = np(1-p)[/tex]
Hence, the probability that the experiment results in exact success are;
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
Learn more about binomial distribution here:
https://brainly.com/question/13609688
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