Could someone please tell me if I am on track with my answer?
Jack is taking a four-item true-false test. He has no knowledge about the subject of the test and decides to flip a coin to answer the items. What is the probability that he receives a perfect score? What is the probability on a 10-item test?
P(coin being correct in a 4 item t or f test) = 2/4
P(coin being correct in a 10 item t or f test) = 2/10 or 1/5
The chance that you get each question correct is 1/2. To calculate the probability of a perfect score on a 4 question test, you muliply the chance for each correct answer, sooo
1/2 X 1/2 X 1/2 X 1/2 = 1/16
On the 10 question test, it would be
1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 = 1/1024
Thank you, you really helped me!
Your very welcome!
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.