To calculate: The probability that there are exactly one correct, exactly two correct answers, and exactly three correct answers among five multiple-choice questions.
The probability that there is exactly one correct answer
The probability that there are exactly two correct answers
The probability that there is exactly three correct answers
Given:
The total number of multiple-choice questions
The total number of choices for each question
The number of the correct answer to a question
Concept used:
The binomial probability distribution X with the total number of trials “n” and probability of success “p” for x success the probability is calculated as shown below:
Calculation:
Consider, X be the random variable that follows the binomial distribution.The probability that a randomly chosen question is marked correct
The total number of multiple-choice questions
The probability that exactly one correct answer is calculated as shown below:
The probability that exactly two correct answers is calculated as shown below:
The probability that exactly three correct answers is calculated as shown below:
The probability that exactly one correct answer, two correct answers, and three correct answers are 0.4096, 0.2048, and 0.0512 respectively.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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