6. A Finite final consists of 30 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 27 or better) by purely guessing on each question.
6. A Finite final consists of 30 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 27 or better) by purely guessing on each question.
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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![**Problem Statement:**
A Finite final consists of 30 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 27 or better) by purely guessing on each question.
**Analysis:**
- Total questions: 30
- Choices per question: 5
- Correct answer chances per question: 1 out of 5
- Target for an 'A': At least 27 correct answers
To solve this problem, one would need to apply binomial probability calculations, focusing on scenarios where the number of successful guesses (correct answers) is 27 or more out of 30. The probability of guessing each question correctly is 0.2 (or 20%).
The problem uses concepts from probability and statistics, specifically the binomial distribution, where:
- \( n = 30 \) (total number of trials - questions)
- \( k = 27, 28, 29, 30 \) (successful outcomes needed for an A)
- \( p = \frac{1}{5} = 0.2 \) (probability of success on a single trial)
- The probability can be calculated using the formula for binomial probability:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where \( \binom{n}{k} \) is the binomial coefficient.
**Note:** Calculating this probability involves determining the cumulative probability for getting 27, 28, 29, or 30 correct answers and summing these probabilities. This generally requires computational software or a binomial distribution calculator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46f2e9fa-ab74-4ca7-bd02-7053ab3372bf%2F7dd72a64-0b4a-4463-a8c4-ee09ad8f0fef%2Fizlt606_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A Finite final consists of 30 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 27 or better) by purely guessing on each question.
**Analysis:**
- Total questions: 30
- Choices per question: 5
- Correct answer chances per question: 1 out of 5
- Target for an 'A': At least 27 correct answers
To solve this problem, one would need to apply binomial probability calculations, focusing on scenarios where the number of successful guesses (correct answers) is 27 or more out of 30. The probability of guessing each question correctly is 0.2 (or 20%).
The problem uses concepts from probability and statistics, specifically the binomial distribution, where:
- \( n = 30 \) (total number of trials - questions)
- \( k = 27, 28, 29, 30 \) (successful outcomes needed for an A)
- \( p = \frac{1}{5} = 0.2 \) (probability of success on a single trial)
- The probability can be calculated using the formula for binomial probability:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where \( \binom{n}{k} \) is the binomial coefficient.
**Note:** Calculating this probability involves determining the cumulative probability for getting 27, 28, 29, or 30 correct answers and summing these probabilities. This generally requires computational software or a binomial distribution calculator.
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