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The problem in the image involves calculating the probability of getting exactly one correct answer when making guesses on a test with 8 questions. This is a binomial probability problem, where:

- \( n = 8 \) (number of trials, or questions),
- \( p = 0.50 \) (probability of success for each trial),
- \( x = 1 \) (number of correct answers we're looking for).

The binomial probability formula is:

\[
P(x) = \binom{n}{x} p^x (1 - p)^{n - x}
\]

For this problem:

\[
P(1) = \binom{8}{1} (0.5)^1 (0.5)^{8 - 1}
\]

I'll now calculate the probability \( P(1) \) for this scenario.The probability of getting exactly one correct answer out of 8 guesses, where the probability of success is 0.5, is approximately **0.031** (rounded to three decimal places).

Would you like more details, or do you have any questions?

Here are 5 related questions you might explore:

1. How would the probability change if we were looking for exactly 2 correct answers?
2. What is the probability of getting no correct answers (i.e., \(P(0)\))?
3. How does the probability change if the number of trials is increased to 10 questions?
4. How would the probability change if the success probability was different, say \(p = 0.6\)?
5. What is the cumulative probability of getting 0, 1, or 2 correct answers?

**Tip:** In binomial problems, the probability \(p\) represents the likelihood of success for each trial. When \(p = 0.5\), each outcome is equally likely, making it useful for modeling scenarios like fair coin tosses.

Assume that guesses are made for 8 questions on a medical admissions test such that the probability of success (correct) is given by p = 0.50, where there are n = 8 trials. Find the probability that the number of correct answers is exactly 1.

Learn how to calculate the binomial probability of getting exactly 1 correct answer out of 8 questions with a success probability of 0.50. This problem uses the binomial probability formula and is suitable for Grades 10-12.

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