Question 345595: A quiz cosists of 20 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 %.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The probability of  successes in  trials where  is the probability of success
on any given trial is given by:
\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k})
Where ) is the number of combinations of things taken at a
time and is calculated by !})
For this problem, since there are 5 possible answers for each question, the probability of success on any given trial is 
70% of 20 is 14, so in order to pass, the test taker must get at least 14 correct. The probability of at least 14 correct is the sum of the probabilities of exactly 14, exactly 15, exactly 16, and so on.
So your calculation becomes:
\ =\ \sum_{i=14}^{20}\,\left(20\cr\ i\right\)\left(0.2\right)^i\left(0.8\right)^{20\,-\,i})
Now doing all of that arithmetic has all of the entertainment value of watching paint dry, so here's a very fast shortcut IF you have Excel or Numbers for MAC. Type in the following exactly: =1-BINOMDIST(13,20,0.2,true)
When you hit enter you will get the result of the summation above. Not quite 2 chances out of a million. Moral of the story -- study for your multiple choice exams.
John
My calculator said it, I believe it, that settles it
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