The problem shown asks for the probability that two multiple-choice questions are answered correctly by random guessing. One question has 6 possible answers, and the other has 3 possible answers.

Solution:

To calculate the probability of guessing both questions correctly:

• The probability of guessing the first question correctly is $\frac{1}{6}$ (since there are 6 possible answers).
• The probability of guessing the second question correctly is $\frac{1}{3}$ (since there are 3 possible answers).

Since these events are independent (one guess doesn't affect the other), the overall probability is the product of the two individual probabilities: $\text{Total Probability} = \frac{1}{6} \times \frac{1}{3} = \frac{1}{18}$

To convert this to a percentage: $\frac{1}{18} \approx 0.0556 = 5.56\%$

Thus, the probability that both responses are correct is 5.6% when rounded to one decimal place.

Would you like further clarification or details on this problem?

Here are 5 related questions:

1. How do you calculate probabilities for more complex problems involving multiple guesses?
2. How do independent events affect probability?
3. What changes if the guesses are not random but based on some strategy?
4. How would this probability change if the number of possible answers per question was increased?
5. Can you explain how dependent events differ from independent ones in probability?

Tip: Always multiply the probabilities of independent events to find the combined probability.