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Q: stats and probability question ( Answered ,   1 Comment )
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 Subject: stats and probability question Category: Reference, Education and News > Homework Help Asked by: jsanders65-ga List Price: \$5.00 Posted: 19 Oct 2005 17:30 PDT Expires: 18 Nov 2005 16:30 PST Question ID: 582365
 ```A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the test?```
 Answer
 Subject: Re: stats and probability question Answered By: leapinglizard-ga on 19 Oct 2005 17:44 PDT Rated:
 ```Dear jsanders65, Since there are 10 questions with 2 possible answers each, there are 2^10 = 1024 ways to complete the test. Now consider the number of ways in which the student can pass the test. He can answer all questions correctly, which is one way. Or he can answer one of 10 questions correctly, which is 10 ways. Or he can answer any two out of 10 questions correctly, which is 10*9/2 = 45 ways. (If you're not convinced by that last calculation, look at it this way. You want to choose a pair of items among 10, so you begin by picking one item, which is a choice among 10. Then you pick another item, which is a choice among the remaining 9. So it seems that there are 10*9 ways to pick a pair among ten, except that half of these selections are the mirror image of the other half. Hence the 10*9/2 = 45 possibilities.) All in all, there are 1 + 10 + 45 = 56 ways to pass the test. Since the student is picking answers randomly, we don't favor any particular outcome, so his chance of passing the test is just 56/1024 = 0.0546875 or about 5.5%. Regards, leapinglizard```
 jsanders65-ga rated this answer: and gave an additional tip of: \$5.00 `you are the best! thank you...`

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 Subject: Re: stats and probability question From: leapinglizard-ga on 19 Oct 2005 18:22 PDT
 ```Thank you for the rating and the kind tip. By the way, I made a pair of typos in my answer that do not affect the calculations. In the last two sentences of the second paragraph, read "incorrectly" for "correctly". The idea is that answering nine questions correctly is the same as answering one incorrectly, and getting eight right is the same as getting two wrong. leapinglizard```
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