If a true-false test with 5 questions is given, what is the probability of scoring (A) Exactly 80% just by guessing? (B) 80% or better by just guessing? (A) P(exactly 80%) (Round to five decimal places as needed.)
If a true-false test with 5 questions is given, what is the probability of scoring (A) Exactly 80% just by guessing? (B) 80% or better by just guessing? (A) P(exactly 80%) (Round to five decimal places as needed.)
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...
Related questions
Question
![**Probability of Scoring by Guessing on a True-False Test**
**Problem Statement:**
If a true-false test with 5 questions is given, what is the probability of scoring:
(A) Exactly 80% just by guessing?
(B) 80% or better by just guessing?
**Solution Approach:**
(A) P(exactly 80%) ≈ [Enter your answer here] (Round to five decimal places as needed.)
**Explanation:**
To solve this problem, use the binomial probability formula, where:
- **n** = number of trials (questions) = 5
- **p** = probability of success on each trial (correct answer by guessing) = 0.5
- **k** = number of successes needed for a particular score
**Calculations:**
- Exactly 80% means 4 correct answers out of 5 (80% of 5).
- The probability for exactly 4 correct answers can be calculated using the binomial probability formula:
\[ P(k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} \]
For more detailed solutions or different probabilities, you can explore binomial probability distribution tables or calculators.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7db70af-c27e-4f00-befb-6689742adb00%2F0b9d40da-0963-46be-bb2b-f18d75f57da8%2Fcl913hj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability of Scoring by Guessing on a True-False Test**
**Problem Statement:**
If a true-false test with 5 questions is given, what is the probability of scoring:
(A) Exactly 80% just by guessing?
(B) 80% or better by just guessing?
**Solution Approach:**
(A) P(exactly 80%) ≈ [Enter your answer here] (Round to five decimal places as needed.)
**Explanation:**
To solve this problem, use the binomial probability formula, where:
- **n** = number of trials (questions) = 5
- **p** = probability of success on each trial (correct answer by guessing) = 0.5
- **k** = number of successes needed for a particular score
**Calculations:**
- Exactly 80% means 4 correct answers out of 5 (80% of 5).
- The probability for exactly 4 correct answers can be calculated using the binomial probability formula:
\[ P(k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} \]
For more detailed solutions or different probabilities, you can explore binomial probability distribution tables or calculators.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON