Question

In history class, Colin takes a multiple-choice quiz. There are 10 questions. Each question has five possible answers. To the nearest percentage, what is the probability that Colin will get exactly 3 questions correct if he guesses an answer to each question?

Answer 1

Well assuming that the test is a 10 point test. 10 meaning one point each test he would get 30%

Answer 2

Answer:

$P = 0.201$

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:

$P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}$

Where:

$p=\frac{1}{5}$

$n=10$

$x=3$

$P(x=3) = \frac{10!}{3!(10-3)!}*(\frac{1}{5})^3*(1-\frac{1}{5})^{10-3}$

$P(x=3) = \frac{10!}{3!*7!}*\frac{1}{125}*(\frac{4}{5})^{7}$

$P = 0.201$