The probability of getting no correct answers can be calculated using the binomial probability formula:

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

where:

• $n = 5$ (number of trials/questions),
• $k = 0$ (number of correct answers),
• $p = 0.5$ (probability of success on each trial).

Plugging in the values:

$P(X = 0) = \binom{5}{0} (0.5)^0 (1 - 0.5)^5$

Calculating each part:

1. $\binom{5}{0} = 1$,
2. $(0.5)^0 = 1$,
3. $(1 - 0.5)^5 = (0.5)^5 = 0.03125$.

Thus,

$P(X = 0) = 1 \times 1 \times 0.03125 = 0.03125$

So, the probability of no correct answers is 0.031 (rounded to three decimal places).

Would you like more details or have any questions?

Here are some related questions to consider:

1. What is the probability of exactly one correct answer?
2. What is the probability of exactly two correct answers?
3. How does increasing the number of choices per question affect the probability of no correct answers?
4. What is the probability of at least one correct answer?
5. How would the probability change if the number of questions increased to 10?

Tip: The binomial probability formula is highly useful in problems with multiple trials and fixed success probabilities.