Since each question has 3 choices and only 1 correct answer, the probability of guessing correctly on any given question is:

$P(\text{correct}) = \frac{1}{3}$

Now, let's calculate the probabilities for each case:

1. Answering the first question correctly
   $P(\text{first correct}) = \frac{1}{3}$

2. Answering the first 2 questions correctly
   Since the events are independent, we multiply probabilities: $P(\text{first 2 correct}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9} \approx 0.111$

3. Answering the first 3 questions correctly
   $P(\text{first 3 correct}) = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27} \approx 0.037$

4. Answering the first 4 questions correctly
   $P(\text{first 4 correct}) = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{81} \approx 0.012$

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Would you like a more detailed explanation or visualization? Here are some related questions to explore:

1. What is the probability of getting at least one question correct out of four?
2. How does the probability change if there are 4 answer choices per question instead of 3?
3. What is the probability of answering exactly two out of four questions correctly?
4. How many questions would you expect to answer correctly if you guessed on a 10-question quiz?
5. How would the probabilities change if you could eliminate one wrong answer before guessing?

Tip: The probability of a sequence of independent events happening is found by multiplying their individual probabilities.