In a multiple choice exam consisting of 5 questions, each with 4 possible answers, what is the likelihood that a student answers 3 or more questions correctly? Each question has one correct answer, and the student has an equal chance of selecting any of the four options.

Answer Choices

Correct answer marked below

24/256

53/512

Correct

105/512

459/512

47/256

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

In this multiple choice exam with 5 questions and 4 choices per question, the probability of selecting the correct answer (C) is 1/4, while the probability of selecting an incorrect answer (W) is 3/4. We need to calculate the probability of getting at least 3 correct answers: The probability of getting exactly 3 correct answers out of 5 is given by

\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2

, which accounts for the different arrangements of 3 correct and…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

What this question tests

What it tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Common trap

Forgetting to use the complement for 'at least one', or treating dependent events as independent.