Question

A multiple choice test has 5 questions, each with 4 choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question without reading the question.

1.) What is the probability that you answer all 5 questions correctly?
2.) What is the probability that you do not answer any of the 5 questions correctly?
3.) What is the probability that you answer at least one of the 5 questions correctly?

Answer 1

The probability of answering all 5 questions correctly is 1/1024, the probability of not answering any of the questions correctly is 243/1024, and the probability of answering at least one question correctly is 781/1024.

Step-by-step explanation:

To find the probability of answering all 5 questions correctly, we need to multiply the probabilities of getting each question right. Since there are 4 choices for each question and only 1 is correct, the probability of getting a single question right is 1/4.

Therefore, the probability of answering all 5 questions correctly is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = 1/1024.

To find the probability of not answering any of the 5 questions correctly, we need to find the probability of getting each question wrong. Since there are 4 choices for each question, the probability of getting a single question wrong is 3/4.

Therefore, the probability of not answering any of the 5 questions correctly is

(3/4) * (3/4) * (3/4) * (3/4) * (3/4) = 243/1024.

To find the probability of answering at least one question correctly, we can subtract the probability of not answering any of the 5 questions correctly from 1.

Therefore, the probability of answering at least one question correctly is 1 - 243/1024 = 781/1024.