Amit is going to guess on all $20$ questions of his multiple-choice test. Each question on the test has $4$ answer options, and only one is correct. $\newline$ What is the best prediction for the number of questions that Amit will answer correctly? $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $5$ questions $\newline$ (B) Close to $5$ questions but probably not exactly $5$ questions $\newline$ (C) Exactly $80$ questions $\newline$ (D) Close to $80$ questions but probably not exactly $80$ questions

Full solution

Q. Amit is going to guess on all

20

questions of his multiple-choice test. Each question on the test has

4

answer options, and only one is correct.

\newline

What is the best prediction for the number of questions that Amit will answer correctly?

\newline

Choose

1

answer:

\newline

(A) Exactly

5

questions

\newline

(B) Close to

5

questions but probably not exactly

5

questions

\newline

80

questions

\newline

(D) Close to

80

questions but probably not exactly

80

questions

Understand the problem: Understand the problem. $\newline$ Amit is guessing on a multiple-choice test with $20$ questions. Each question has $4$ answer options, and only one option is correct. We need to predict how many questions Amit will answer correctly by guessing.
Calculate probability: Calculate the probability of guessing a question correctly. Since there are $4$ answer options and only one is correct, the probability of guessing a question correctly is $1$ out of $4$ , or $\frac{1}{4}$ .
Use probability to predict: Use the probability to predict the number of correct answers. $\newline$ To find the expected number of correct answers, multiply the probability of getting a question right $\frac{1}{4}$ by the total number of questions $20$ . $\newline$ Expected number of correct answers = $\frac{1}{4} \times 20$
Perform the calculation: Perform the calculation. $\newline$ Expected number of correct answers = $0.25 \times 20$ $\newline$ Expected number of correct answers = $5$
Interpret the result: Interpret the result. $\newline$ The calculation shows that the best prediction for the number of questions Amit will answer correctly is $5$ . However, since guessing introduces variability, it is unlikely to be exactly $5$ . The prediction is that it will be close to $5$ questions.