To determine if your answer is correct, we need to use the concept of probability. In this case, since the test is multiple choice with only two possible answers (true or false), we can calculate the probability of getting a correct answer by flipping a coin.
For a four-item test, you correctly identified that the probability of getting a single item correct by flipping a coin is 2/4. Since each item is independent, meaning the outcome of one item does not affect the outcome of another, we can multiply the probabilities to find the probability of getting a perfect score on the entire test.
Therefore, the probability of getting a perfect score on a four-item test is (2/4)^4, which simplifies to 1/16 or approximately 0.0625.
For a ten-item test, you correctly identified that the probability of getting a single item correct by flipping a coin is 2/10 or 1/5. Again, since each item is independent, we can multiply the probabilities to find the probability of getting a perfect score on the entire test.
Therefore, the probability of getting a perfect score on a ten-item test is (1/5)^10, which simplifies to 1/9765625 or approximately 0.000000102.