by Guest » Fri Mar 20, 2020 4:46 pm
Don't feel bad. The question isn't well formed in my opinion. Probabilities assume random distributions but errors on a math test are not random errors, they are errors in process/logic. Putting that aside, we'll assume each of the 20 question in fact had 3 wrong options and 1 correct option and options would be chosen at random by any person taking the test. Then, the probability of making a specific choice (correct or not) on any given question is 1/4. For two persons to answer all questions the same way (with completely random selections) would require they match on question 1 AND they match on question 2 AND they match on question 3 AND...(all the way to question 20). In considering compound probabilities the AND is represented by multiplying the two individual probabilities. So, the chance of two persons matching on question 1 is (1/4)*(1/4)....to match on question 2 is also (1/4)*(1/4)...and so on. But, to match on question 1 AND question 2 has a chance of (1/16)*(1/16).
So, to match all 20 with complete random choices would be [tex](1/16)^{20}[/tex]...and that's just two persons. Integrating the 3rd person is left for you.
Don't feel bad. The question isn't well formed in my opinion. Probabilities assume random distributions but errors on a math test are not random errors, they are errors in process/logic. Putting that aside, we'll assume each of the 20 question in fact had 3 wrong options and 1 correct option and options would be chosen at random by any person taking the test. Then, the probability of making a specific choice (correct or not) on any given question is 1/4. For two persons to answer all questions the same way (with completely random selections) would require they match on question 1 AND they match on question 2 AND they match on question 3 AND...(all the way to question 20). In considering compound probabilities the AND is represented by multiplying the two individual probabilities. So, the chance of two persons matching on question 1 is (1/4)*(1/4)....to match on question 2 is also (1/4)*(1/4)...and so on. But, to match on question 1 AND question 2 has a chance of (1/16)*(1/16).
So, to match all 20 with complete random choices would be [tex](1/16)^{20}[/tex]...and that's just two persons. Integrating the 3rd person is left for you.