Dangerous Quiz
There are 10 true/false questions in a quiz. You don't know any answers. You guess randomly. The paper comes back. You need to answer half of the questions correctly to pass. You look at the first page. There are 4 correct answers and 4 wrong answers. Given that the probability that you answer a question correctly is 0.5, what is the probability that you pass the test?
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1 solution
As yoy already have 4 correct answers, you need one more to pass. You can only fail if both the answers are wrong, which the probability ia 0.5×0.5=0.25. 1-0.25=0.75. Thus the probability that you pass is 0.75.