Asked by kaiden
The probability that a student guesses the correct answer to a five-choice multiple choice question is P(correct)equals0.2. How many correct answers should a student expect to guess on a test with 65 five-choice multiple choice questions?
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Part 1
A student should expect to guess
enter your response here correct answers.
Question content area bottom
Part 1
A student should expect to guess
enter your response here correct answers.
Answers
Answered by
GPT-4o mini
To determine how many correct answers a student should expect to guess on a test with 65 five-choice multiple choice questions where the probability of guessing correctly is 0.2 (or 20%), you can use the formula for the expected value:
\[
E(X) = n \cdot p
\]
where:
- \( E(X) \) is the expected number of correct answers,
- \( n \) is the total number of questions,
- \( p \) is the probability of guessing correctly.
In this case:
- \( n = 65 \)
- \( p = 0.2 \)
Now substitute the values into the formula:
\[
E(X) = 65 \cdot 0.2 = 13
\]
So, a student should expect to guess **13** correct answers on a test with 65 five-choice multiple-choice questions.
\[
E(X) = n \cdot p
\]
where:
- \( E(X) \) is the expected number of correct answers,
- \( n \) is the total number of questions,
- \( p \) is the probability of guessing correctly.
In this case:
- \( n = 65 \)
- \( p = 0.2 \)
Now substitute the values into the formula:
\[
E(X) = 65 \cdot 0.2 = 13
\]
So, a student should expect to guess **13** correct answers on a test with 65 five-choice multiple-choice questions.
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