Binomial event is the event in which the probability of the success of a trial in a fixed number of trials is definite.The probability of binomial event to be success 12 times in 20 trials is 0.0001017. Thus the option A is the correct option.
A binomial event has n 20 trials
The probability of success for each trial is [tex]p[/tex] 0.20.
Total number of the trials is 20.
Binomial event is the event in which the probability of the success of a trial in a fixed number of trials is definite.
The probability of the failure for each trial is,
[tex]q=1-0.20=0.8[/tex]
Binomial distribution formula can be given as,
[tex]P=\dfrac{n!}{(n-x)!x!} (p^xq^{n-x})[/tex]
[tex]P=\dfrac{20!}{(20-12)!12!} ((0.2)^{12}\times0.8^{20-12})[/tex]
[tex]P=\dfrac{20!}{8!12!} ((0.2)^{12}\times0.8^{8})[/tex]
[tex]P=0.0001017[/tex]
Thus the probability of binomial event to be success 12 times in 20 trials is 0.0001017. Thus the option A is the correct option.
Learn more about the binomial event here;
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