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Sveta_85 [38]
2 years ago
13

If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of g

etting at least 1 correct? if a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing?
Mathematics
1 answer:
QveST [7]2 years ago
4 0
There is a 1/5 chance of getting each question correct.  The probability of getting <em>at least</em> 1 correct is written as such:
<em>P</em>(<em>X</em> ≥ 1) = 1 - <em>P</em>(<em>X</em> = 0) 
This is because the only other option than getting at least one correct is to get nothing correct.
Since there is a 1/5 chance of getting each question correct, there is a 4/5 chance of getting each question wrong:
1 - <em>P</em>(<em>X</em> = 0) = 1 - (4/5)^10 (since there are 10 questions, with a 4/5 chance of missing each one)
= 1 - 0.1073741824 ≈ 0.8926 = 89.26% chance of getting at least one question correct.  Given this probability, it is reasonable to expect to pass by guessing.
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