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?

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?
~~~~~~~~~~~~~~~

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?

Then the answer is   .

Answer by rothauserc(4718)   (Show Source): 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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