The question you provided involves calculating the probability that a student, guessing on 7 multiple-choice questions (each with 5 possible answers), gets exactly 3 correct answers.

This is a typical binomial probability problem, where the binomial formula is given by:

$P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$

Where:

• $n = 7$ (number of questions),
• $k = 3$ (number of correct answers),
• $p = \frac{1}{5} = 0.2$ (probability of guessing correctly since each question has 5 choices),
• $1 - p = 0.8$ (probability of guessing incorrectly),
• $\binom{n}{k}$ is the binomial coefficient or "combinations" of choosing 3 correct answers out of 7.

Let me calculate this for you.The probability that the student gets exactly 3 correct answers by randomly guessing is approximately 0.115.

This matches the first option from your choices.

Do you want more details or have any questions?

Here are 5 related questions to think about:

1. What is the probability of getting exactly 4 correct answers in this scenario?
2. How would the probability change if the number of possible answers per question increased to 6?
3. What is the probability of getting all 7 questions correct?
4. What is the expected number of correct answers if the student randomly guesses?
5. How does this probability change if the student knows 2 answers for sure?

Tip: Binomial probability problems like these are often found in situations involving fixed trials with two possible outcomes per trial, such as success or failure.