Answer:
[tex]P = 0.201[/tex]
Step-by-step explanation:
If the discrete random variable X represents the number of correct Colin responses then X can be represented by a binomial distribution with parameters p, n, x.
In this case p represents the probability that colin gets a correct answer, n represents the number of questions.
So the probability that Colin receives x correct questions is:
[tex]P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]
Where:
[tex]p=\frac{1}{5}[/tex]
[tex]n=10[/tex]
[tex]x=3[/tex]
[tex]P(x=3) = \frac{10!}{3!(10-3)!}*(\frac{1}{5})^3*(1-\frac{1}{5})^{10-3}[/tex]
[tex]P(x=3) = \frac{10!}{3!*7!}*\frac{1}{125}*(\frac{4}{5})^{7}[/tex]
[tex]P = 0.201[/tex]
