Question

Multiple-choice questions each have 5 possible answers, one of which is correct. assume that you guess the answers to 4 such questions. use the multiplication rule to find the probability that the first three guesses are wrong and the fourth is correct. that is, find p ( x
c. , where c denotes a correct answer and w denotes a wrong answer.

Answer 1

Independent Multiplication Rule:
P(X = w, w, w, c) = P(w) ∩ P(w) ∩ P(w) ∩ P(c)

Therefore,
P(X = w, w, w, c) = (1/5) • (1/5) • (1/5) • (1/5)
P(X = w, w, w, c) = 1/(5^4) = 1/625 or 0.16%