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In a twenty question true false examination a student must achieve eight correct answers to pass if student answers randomly what is the probability that student will fail?
Wiki User
∙ 14y ago
The probability this student will fail is the same as the probability that some other student will flip a fair coin 20 times and get less than 8 heads, i.e., more than 12 tails.
There are 2^20 possible different-looking sequences of 20 coinflips, which we assume all have equal probability.
Of those sequences, 1 has no heads at all, 20 have exactly 1 head, 190 have exactly 2 heads, ... and 77520 have exactly 7 heads.
So we sum up all those possible ways to fail and we get ...
... ...
I'm assuming that the student answers randomly, flipping a fair (50:50) coin on each question to choose "true" or "false".
In that special case, it doesn't matter how many of those twenty questions are true or how many are false.
(If the student answers randomly by flipping an unfair coin, say a 25:75 coin, then it does matter how many of those questions are true -- I'll let you figure that one out).
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∙ 14y ago
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