SOLUTION: A multiple choice quiz has 5 questions. Each question has 4 choices. What is the probability of randomly guessing on all questions and getting them all correct?
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Question 1095645: A multiple choice quiz has 5 questions. Each question has 4 choices. What is the probability of randomly guessing on all questions and getting them all correct? Found 2 solutions by ikleyn, rothauserc:Answer by ikleyn(52786) (Show Source):
You can put this solution on YOUR website! .
A multiple choice quiz has 5 questions. Each question has 4 choices.
What is the probability of randomly guessing on all questions and getting them all correct?
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Actually, this condition is incomplete, since it doesn't say how many of each of 4 choices are correct.
In principle, it may happen that all of them are incorrect.
Or, let say, 3 of them are correct.
Or even all 4 are correct.
I perfectly understand what the author was going to say in the condition (but failed to say). The correct formulation is THIS:
A multiple choice quiz has 5 questions. Each question has 4 choices, of which only one is correct.
What is the probability of randomly guessing on all questions and getting them all correct?
You can put this solution on YOUR website! We use the binomial probaility distribution to answer this problem
:
Probability(P) (k successes out of n trials) = nCk * p^k * (1-p)^(n-k) where p is probability of a success and nCk - n! / (k! * (n-k)!)
:
p = 1/4 = 0.25
:
P (5 successes out of 5 trials) = (5! / (5! * (5-5)!) * (0.25)^5 * (1-0.25)^(5-5) =
:
1 * (0.25)^5 * 1 = 0.000976562 approximately 0.001
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