SOLUTION: A class of 18 students are taking an exam. The probability of passing an exam is higher than the probability of failing. If the probability that half the students pass the exam

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Question 1116434: A class of 18 students are taking an exam. The
probability of passing an exam is higher than the
probability of failing. If the probability that half the
students pass the exam is 0.0642543198, find the
probability of passing the exam.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The probability that 9 of 18 students pass, if the probability of passing is p and the probability of failing is (1-p), is

C%2818%2C9%29p%5E9%281-p%29%5E9

So we have

C%2818%2C9%29p%5E9%281-p%29%5E9+=+.0642543198
p%5E9%281-p%29%5E9+=+1.321561493%2A10%5E-6
p%281-p%29+=+%281.321561493%2A10%5E-6%29%5E%281%2F9%29+=+2%2F9

This is more easily solved by inspection than by formal algebra: p = 2/3, 1-p = 1/3.

Answer: The probability of passing the exam is 2/3.