SOLUTION: An unprepared student makes random guesses for 6 multiple choice questions that have selections a - e. Find the probability that there is at least one correct answer
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Question 321724: An unprepared student makes random guesses for 6 multiple choice questions that have selections a - e. Find the probability that there is at least one correct answer
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 !})
The probability your student got at least one correct is equal to 1 minus the probability that he missed them all, which is to say 1 minus the probability that he got zero correct. You want the probability of zero successes in six trials where the probability of success on a given trial is one-fifth, or 0.2.
\ =\ 1\ -\ P_6(0)\ =\ 1\ -\ \left(6\cr 0\right\)\(0.2)^0\left(0.8\right)^{6})
You get to do your own arithmetic. Hint: \ =\ 1)
for all positive integers 
.
John
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