vitor is going to guess on all 40 questions of his multiple - choice test. each question on the test has 5…

vitor is going to guess on all 40 questions of his multiple - choice test. each question on the test has 5 answer options. complete the following statement with the best prediction. vitor will correctly answer... choose 1 answer: a exactly 8 questions b close to 8 questions but probably not exactly 8 questions c exactly 20 questions d close to 20 questions but probably not exactly 20 questions

vitor is going to guess on all 40 questions of his multiple - choice test. each question on the test has 5 answer options. complete the following statement with the best prediction. vitor will correctly answer... choose 1 answer: a exactly 8 questions b close to 8 questions but probably not exactly 8 questions c exactly 20 questions d close to 20 questions but probably not exactly 20 questions

Answer

Explanation:

Step1: Calculate probability of correct answer

The probability of getting a single - multiple - choice question correct by guessing when there are 5 options is $p=\frac{1}{5}=0.2$.

Step2: Calculate expected number of correct answers

The number of questions $n = 40$. The expected value of the number of correct answers $E(X)=np$. Substituting $n = 40$ and $p=0.2$, we get $E(X)=40\times0.2 = 8$.

Step3: Consider the nature of probability

The expected value is just an average over a large number of trials. In a single set of 40 guesses, we are likely to be close to 8 correct answers but not exactly 8 due to the random nature of guessing.

Answer:

B. Close to 8 questions but probably not exactly 8 questions