Respuesta :
Answer:
Step-by-step explanation:
[tex]10C_{7}\times (0.2)^{7} \times (0.8)^{3}\\[/tex]
The probability that a student guesses the correct answer to exactly 7 questions is 0.004.
What is binomial probability?
The probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes is called binomial probability.
Binomial probability formula
[tex]P_{x} =nC_{x} P^{x} q^{n-x}[/tex]
where,
P is binomial probability
x is number of times for a specific outcome within n trials
[tex]nC_{x}[/tex] number of combinations
p is probability of success on a single trial
q is probability of failure on a single trial
n is number of trials
According to the given question.
A test consisted of 10 multiple choices.
⇒ Number of trials, n = 10
The student have to give exactly 7 correct answers.
⇒ x = 7
The probability of being correct in one trial, p = [tex]\frac{1}{5}[/tex]
(only one option is correct among fives)
So, the probability of being incorrect/wrong in one trial, q = [tex]1-\frac{1}{5} =\frac{4}{5}[/tex]
Therefore, the probability that a student guesses the correct answer to exactly 7 questions is given by
[tex]P_{x} = 10C_{7} (\frac{1}{5}) ^{7} (\frac{4}{5} )^{3}[/tex]
⇒ [tex]P_{x} = \frac{10!}{7!3!} (0.2)^{7}( 0.8)^{3}[/tex]
⇒[tex]P_{x} = 120(0.0000128)(0.512)[/tex]
⇒ [tex]P_{x} =0.004[/tex]
Hence, the probability that a student guesses the correct answer to exactly 7 questions is 0.004.
Find out more information about binomial probability here:
https://brainly.com/question/12474772
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