Jack is taking a four-item true-false test. He has no knowledge about the subject of the test and decided 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?
Answer: 1/16 or 6.25% that he receives a perfect score .
1/1,024 0r .000976562% not likely of a perfect score on the 10-item test.
Is this correct?
Thanks.
Yes, however, this assumes the probabily of true and false answers are equal. On real tests, that is not true.
on the second, you did not covert the correct fraction to percent.
How would I convert the correct fraction on the second answer? Thanks for your help.
Wouldn' the second fraction convert to 9.8%?
Yes, your answer is correct. Let me explain how you arrived at these probabilities.
For a four-item true-false test, Jack decides to use a coin flip to answer each item. Since there are two possible outcomes (true or false) for each item, there are a total of 2^4 = 16 possible combinations of answers that Jack can have.
To find the probability of receiving a perfect score, we need to determine the number of favorable outcomes (i.e., the number of ways Jack can answer all four items correctly) out of the total number of possible outcomes. In this case, there is only one favorable outcome, which is when Jack gets all four items correct (HHHH, where H represents a heads result from the coin flip). Therefore, the probability of getting a perfect score is 1/16 or 6.25%.
For a ten-item true-false test, the same logic applies. There are 2^10 = 1,024 possible combinations of answers. However, the number of favorable outcomes (all correct answers) remains only one (HHHHHHHHHH). Therefore, the probability of getting a perfect score on a ten-item test is 1/1,024 or approximately 0.000976562%. It is highly unlikely to achieve a perfect score on this test using a coin flip method.
So, your probabilities are indeed correct.