Each question of a 5-question multiple choice exam has 5 possible answers. Suppose a student picks an answer at random for each question. Find the probability the student selects the correct answer on none of the questions. The probability that none of the questions are answered correctly is (Simplify your answer. Type an integer or a fraction.)
Each question of a 5-question multiple choice exam has 5 possible answers. Suppose a student picks an answer at random for each question. Find the probability the student selects the correct answer on none of the questions. The probability that none of the questions are answered correctly is (Simplify your answer. Type an integer or a fraction.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Probability of Randomly Guessing Multiple-Choice Answers
**Problem Statement:**
Each question of a 5-question multiple-choice exam has 5 possible answers. Suppose a student picks an answer at random for each question. Find the probability the student selects the correct answer on none of the questions.
**Prompt:**
The probability that none of the questions are answered correctly is [ ].
(Simplify your answer. Type an integer or a fraction.)
**Instructions:**
Students are asked to calculate the probability of selecting the wrong answer for all the questions in a 5-question test where each question has 5 possible answers.
**Solution Approach:**
1. **Probability of Incorrect Answer for One Question:**
- There are 5 possible answers.
- Only 1 answer is correct.
- Probability of an incorrect answer for one question = 4/5.
2. **Probability of Incorrect Answers for All 5 Questions:**
- Apply the rule of multiplication for independent events.
- Probability = (4/5) * (4/5) * (4/5) * (4/5) * (4/5) = (4/5)^5.
3. **Simplification:**
- Calculate (4/5)^5 to find the simplified probability.
**Interactive Components:**
- A box to type in the final answer.
- "Clear all" button to reset inputs.
- "Check answer" button to verify the entered solution.
Students should engage with the practice tools provided to test their calculations and verify their understanding of probability concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c711c79-350e-448c-80fc-5638f7277d94%2F76045b2c-fe9b-4edb-bcdc-a9e54356fa8f%2Fwj8a0b9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability of Randomly Guessing Multiple-Choice Answers
**Problem Statement:**
Each question of a 5-question multiple-choice exam has 5 possible answers. Suppose a student picks an answer at random for each question. Find the probability the student selects the correct answer on none of the questions.
**Prompt:**
The probability that none of the questions are answered correctly is [ ].
(Simplify your answer. Type an integer or a fraction.)
**Instructions:**
Students are asked to calculate the probability of selecting the wrong answer for all the questions in a 5-question test where each question has 5 possible answers.
**Solution Approach:**
1. **Probability of Incorrect Answer for One Question:**
- There are 5 possible answers.
- Only 1 answer is correct.
- Probability of an incorrect answer for one question = 4/5.
2. **Probability of Incorrect Answers for All 5 Questions:**
- Apply the rule of multiplication for independent events.
- Probability = (4/5) * (4/5) * (4/5) * (4/5) * (4/5) = (4/5)^5.
3. **Simplification:**
- Calculate (4/5)^5 to find the simplified probability.
**Interactive Components:**
- A box to type in the final answer.
- "Clear all" button to reset inputs.
- "Check answer" button to verify the entered solution.
Students should engage with the practice tools provided to test their calculations and verify their understanding of probability concepts.
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