To determine the probability of guessing all the questions correctly in a multiple choice test with 5 questions, where each question has 5 possible answers, we can follow these steps:
First, for each question, there is 1 correct answer out of 5 options. Therefore, the probability of guessing the correct answer for one question is:
P(correct answer) = 1/5
Since the questions are independent, to find the probability of guessing all 5 questions correctly, we need to multiply the probabilities of guessing each question correctly:
P(all correct) = P(question 1) × P(question 2) × P(question 3) × P(question 4) × P(question 5)
Substituting in the value we calculated earlier:
P(all correct) = (1/5) × (1/5) × (1/5) × (1/5) × (1/5) = (1/5)^5
This simplifies to:
P(all correct) = 1/3125
Thus, the probability of guessing all 5 questions correctly is indeed 1 in 3125, or 0.032%. This demonstrates how difficult it is to guess correctly in a multiple choice format when the number of options increases.