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?
The probability of getting the correct answer is 1/2
The probability of getting 4 correct in a row, to make a perfect on a 4 question test, can be found by (1/2)^4, or 1/16.
What do you think the probability of getting a perfect on a 10-item test?
(1/2)^10= 1/1024?
To find the probability of Jack receiving a perfect score on a four-item true-false test by flipping a coin, you need to consider the number of possible outcomes that result in a perfect score, divided by the total number of possible outcomes.
Since Jack has no knowledge about the subject and decides to flip a coin for each item, there are two possible outcomes for each item: heads (H) or tails (T). Therefore, the total number of possible outcomes is 2^4 = 16.
Now, let's determine how many of these outcomes will result in a perfect score. For Jack to score perfectly, he needs to get all four items correct, which means he needs to get heads for all four items (HHHH). There is only one outcome that results in a perfect score.
So, the probability of Jack receiving a perfect score on a four-item test is 1/16.
Now, let's consider a 10-item true-false test. Using the same methodology, there are two possible outcomes for each item, resulting in a total of 2^10 = 1024 possible outcomes.
For Jack to receive a perfect score on this 10-item test, he needs to get all ten items correct, which means he needs to get heads for all ten items (HHHHHHHHHH). There is only one outcome that results in a perfect score.
Therefore, the probability of Jack receiving a perfect score on a ten-item test is 1/1024.