In this case, for each question, there is one correct answer and three incorrect answers, so the probability of answering any given question correctly is:

$P(\text{correct answer}) = \frac{1}{4} = 0.25$

And the probability of answering a question incorrectly is:

$P(\text{incorrect answer}) = \frac{3}{4} = 0.75$

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

1. Probability of answering the first question correctly:

   • Since the probability of answering one question correctly is $0.25$, the probability of answering the first question correctly is:

   $P(\text{first question correct}) = 0.25$

2. Probability of answering the first 2 questions correctly:

   • The probability of answering both the first and second questions correctly is the product of the probabilities for each:

   $P(\text{first 2 correct}) = 0.25 \times 0.25 = 0.0625$

3. Probability of answering the first 3 questions correctly:

   • Similarly, the probability of answering the first three questions correctly is:

   $P(\text{first 3 correct}) = 0.25 \times 0.25 \times 0.25 = 0.015625$

4. Probability of answering the first 4 questions correctly:

   • Finally, the probability of answering all four questions correctly is:

   $P(\text{first 4 correct}) = 0.25 \times 0.25 \times 0.25 \times 0.25 = 0.00390625$

Now, rounding all the answers to four decimal places:

1. Probability of answering the first question correctly: 0.2500
2. Probability of answering the first 2 questions correctly: 0.0625
3. Probability of answering the first 3 questions correctly: 0.0156
4. Probability of answering the first 4 questions correctly: 0.0039

Let me know if you'd like further clarification or more details!

5 Related Questions:

1. What is the probability of answering 5 questions correctly?
2. If there are 10 questions, what is the probability of answering all 10 correctly?
3. How does the probability change if there are more than 4 answer choices per question?
4. What is the probability of answering at least 1 question correctly?
5. How would the probability be affected if there were 5 choices per question instead of 4?

Tip:

When calculating the probability of multiple independent events happening in sequence (like answering multiple questions correctly), you can multiply the individual probabilities together.