Probability of passing a test by guessing
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You can put this solution on YOUR website!
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The events "pass an exam" and "fail to pass the exam" are COMPLEMENTARY events.
You either "pass an exam" or "fail to pass the exam", according to common sense of these words. *)
The sum of probabilities of these events is equal to 1.
Therefore, the probability of failing = 1 - probability of passing = 1 - 0.16 = 0.84. ANSWER
And it is true for any exam - not necessary consisting of 30 questions and not necessary consisting
of multiple choice questions.
The truth is
if the probability of passing an exam is 0.16, then the probability of failing the exam is the COMPLEMENT to it
and is equal to 1- 0.16 = 0.84.
The rest of the words in the post are placed intently to confuse the reader.
-------------- *) In my solution above, I do not consider that case, for example, when answering, let say, more than 20 arbitrary questions of 30 is declared as "passing", but answering, less or equal than 20 questions is NOT necessary considered as failing. Such situation is ALSO may happen in the life --- but it is a special case, which, as a special, should be specified by the rules. In the area of common sense, the events "pass" and "fail to pass" are complementary, by default. If the common sense is violated, than other rules should work --- and then they MUST BE declared in Math problem. Otherwise, it is not a Math problem. There are levels of incorrectness. Some choices are more wrong than others. In test-development language, these incorrect answers are called distractors, because they distract you from the correct answer. You may find one choice that is almost correct, but not quite right. Another choice may be completely incorrect. And the third choice may be almost right, almost wrong, or totally incorrect. Show If you think you know the correct answer without even looking at the other choices, you're probably right. Most studies have shown that your first instinct is usually correct. Those who do poorly on multiple-choice tests are those who overanalyze the question. They think they know the answer, but then start to question their choice. For example, if you were asked the following question, what would you select? The Washington Monument is located in A. the state of Washington. B. New York City. C. Washington, D.C. D. Chicago. The correct choice would be C, Washington, D.C. However, the overthinker starts to get concerned and thinks, "This question is too easy. I wonder if it's asking about some other Washington Monument-maybe there's another one in Washington state." Now, this is a very simplistic example, but it is actually what happens to you if you analyze a question too much. Read the question for what it is. The questions are not tricky. The trick is in choosing the answers. Because you don't lose any points for guessing, understanding how to guess and improve your odds is helpful. The multiple-choice questions on this test have four choices, so your odds are 1 out of 4 that you can pick correctly. To put it another way, you have a 25 percent chance of guessing correctly. These aren't great odds, so you have to find a way to increase them. To do so, you use the process of elimination. Start by eliminating any answers that you know are completely incorrect. In the earlier question, you might be reasonably sure that the Washington Monument isn't located in Chicago, so you can eliminate choice D. Now you have to select the correct answer out of only three choices-1 out of 3, or 33 percent. You've just increased your odds from 25 percent to 33 percent. How do you get to the next level? Suppose that you know that the Washington Monument is on the East Coast. You can eliminate Washington state. You only have two choices-1 out of 2, 50 percent. The odds are getting better. You may be confused as to whether the Washington Monument is in New York City or Washington, D.C., but you can take a guess, and you have a reasonable chance of guessing correctly. Of course, if you knew the answer immediately, you got it right-and that's 100 percent. How can you use this technique to increase your score on the entire test? For example, there are 225 questions on the pencil/paper ASVAB. If you know the answers to 150 questions, you've already reached a score of 66 percent. That leaves only 100 questions for which you don't know the answers immediately. It is important, however, that you answer all of the questions on the test, and now you can make educated guesses. If you can increase your odds to 50 percent on each of the questions you're not sure about, you've now answered another 50 questions correctly-a total of 185 out of 225 questions-a score of 82 percent. Not bad. Therefore, it makes sense to guess. Whether it's an educated guess or just a blind guess, you increase your odds of improving your score on every question. What are odds of guessing on a 50 question test?Assuming that you're guessing on each question, so that the probability of getting any given question right is 12, the probability of guessing right on all 50 questions is (12)50. This is a little more than 8.88×10−16.
How many questions can you get right by guessing?If multiple answers are randomly listed respective to each question and responses to questions are randomly guessed, The probability of a correct response to each question = 1/4. The probability of guessing all 20 questions correctly = (1/4)^20 = 1/1,099,511,627,776.
How does guessing affect reliability?Previous studies have established that chance success due to guessing contributes to error variance and diminishes the reliability of multiple-choice tests and true-false tests.
Is it okay to guess on a test?Yes, you should (probably) guess!
Very few tests today, however, penalize random guesses. A notable exception is the SSAT, a test required for boarding schools and some private schools. For any standardized test, especially more specialized exams, make sure to read the official instructions in case there is a penalty.
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