SOLUTION: An instructor gives a pop quiz consisting of 10 multiple choice questions, where each question has 5 choices, (a) through (e). What is the probability of passing the pop quiz if yo

Question 1055832: An instructor gives a pop quiz consisting of 10 multiple choice questions, where each question has 5 choices, (a) through (e). What is the probability of passing the pop quiz if you guess the answers? Passing means getting 8 out of 10 questions correct.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
This is a binomial probability problem. The probability of success, i.e. getting a question right, is 0.2 (1 out of 5).
The formula is P(x) = C(n,x)*P^x*(1-P)^(n-x) where C(n,x) = n!/(x!(n-x)!), P is the probability of success
We must therefore compute P(8)+P(9)+p(10) since answering 8, 9 or 10 questions correctly results in a passing grade
Using a calculator or spreadsheet, we get P(8)=0.00007373, P(9)=0.000004096, and P(10)=0.0000001024.
The probability of passing is P(8)+P(9)+P(10)=0.00007793, a very unlikely outcome
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