Answer:
81 / 1024
Explanation:
First, let's find the total number of ways that Nancy can choose random choices for the questions. This would be 4 * 4 * 4 * 4 * 4 = 4⁵ = 1024 because there are 4 choices and 5 questions. In order for first question she gets right to be the 5th question, she has to get the first 4 questions wrong. Therefore, since there are 4 choices for each question and only 1 of them is right, she has 4 - 1 = 3 options for the first 4 questions and only 1 option for the 5th one, so the total number of "successful" ways Nancy can do this would be 3 * 3 * 3 * 3 * 1 = 81. Therefore, the probability is 81 / 1024.