What is the probability of getting all ten True or False questions on a test wrong.?

Question

A student took a test with ten True or False questions and managed to get all ten wrong. What were the chances of getting all ten wrong if he did not bother to read the question. Is there a way to "weight" the probability assuming that he did study and that he did read the questions and still got all ten wrong? For instance, without reading the question, the probability of a wrong answer would be 1/2. Can we rate the probability of getting it wrong at 1/4 if he did read and study? If so, what would the probability then be of getting all ten wrong.

Answer 1

to answer the first part... if you do not read any questions on a true or false test and just pick randomly, your chances of getting any one question right or wrong is 0.5, as you said. using the product rule, if the test consists of n questions, the probability of getting all wrong or all false based on random guessing is (1/2)^n. in your case, n=10, so the probability of getting all wrong is 0.5^10 which is 1/1024.

Answer 2

1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2

1/1,024

The odds are 1 out of 1,024.

(Another way of saying that is the odds are 1,023 to 1 against such an event happening.)

Answer 3

This question is quite interesting and it includes many cases. Each case has many ways. For instance, if we assume the student prepare for exam, them how level we can assign for, such as can answer all questions or part of them. If he/she able to solve all of them, then which type of obstacle face? We can assume too many reasons (expected reasons) and others which are may be unexpected reason in the day of exam or even during the test. So, specifying those factors need to be counted firstly and then study probability of happening of each one, then take them within the case of that student to answer the question. If we assume the student was preparing well and the given question within his/her ability/level to answer them with NO obstacle then the probability to get all of them wrong would be zero. But if we assume only the time limited would be the obstacle to answer all the question correctly then we should at beginning specify this factor (time) to account it in the calculation, and so on.

Regards,