SOLUTION: A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. What is the pr
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Question 568750: A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. What is the probability that you answer at least one of the questions correctly?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A multiple-choice test has five questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. What is the probability that you answer at least one of the questions correctly?
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Binomial Problem with n = 5 and p(correct) = 1/5
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P(at least one correct) = 1 - P(none correct)
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= 1 - (4/5)^5
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= 1 - 0.32768
===
= 0.67232
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Cheers,
Stan H.
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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\)\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of combinations of things taken at a time and is calculated by !})
The problem you have is that in order to calculate the probability of "at least one" you would need the probability of exactly 1 plus the probability of exactly 2 plus ... and so on.
Easier is to realize that the probability of getting zero right and the probability of getting at least one right cover all of the possibilities. That is the probability of getting exactly zero correct plus the probability of getting at least one correct is equal to 1. Hence:
\ =\ 1\ -\ P_5(0,0.2)\ =\ 1\ -\ \left(5\cr 0\right\)\left(0.2\right)^0\left(0.8\right)^{5})
Hint:
\ =\ \left(n\cr n\right\)\ =\ 1)
and
John
My calculator said it, I believe it, that settles it
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