Richard has been given a 5-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he does not know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all five questions, find the probability that he will answer all questions incorrectly. Round your answer to the nearest thousandth.

Question

Richard has been given a 5-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he does not know any of the answers. The success occurs if Richard answers a question correctly and the failure occurs if Richard is unable to answer a question correctly. Assuming that Richard guesses on all five questions, find the probability that he will answer all questions incorrectly. Round your answer to the nearest thousandth.

my answer was 0.500 which was wrong please help
0.237
0.410
0.800
0.750
0.5 0.500

Answer 1

the probability that all events would occur is found by multiplying the probabilities of the individual events.

(3/4)^5 = ?

Answer 2

To find the probability that Richard answers all questions incorrectly, we need to consider the probability of him getting each question wrong.

Since each question has four possible answers and only one is correct, the probability of Richard guessing the wrong answer on a single question is 3/4 (since there are 3 incorrect answers out of 4 options).

Since there are 5 questions in total, and Richard is guessing on all of them independently, we can multiply the probabilities together to find the probability of him getting all questions wrong.

Probability of getting a single question wrong = 3/4

Probability of getting all 5 questions wrong = (3/4)^5

Calculating this probability, we get:

(3/4)^5 ≈ 0.237

Therefore, the correct answer is 0.237, rounded to the nearest thousandth.

Answer 3

To find the probability that Richard will answer all questions incorrectly, we need to calculate the probability of him selecting an incorrect answer for each question and multiply those probabilities together.

Since each question has four possible answers and only one is correct, the probability of Richard selecting an incorrect answer for each question is 3/4 or 0.75.

So, to find the probability of answering all five questions incorrectly, we multiply the probability of answering incorrectly for each question:

P(Incorrect answer) = 0.75
P(Incorrect answer for all 5 questions) = (0.75) * (0.75) * (0.75) * (0.75) * (0.75)
= 0.75^5
= 0.2373046875

Rounded to the nearest thousandth, the probability that Richard will answer all questions incorrectly is approximately 0.237. Therefore, the correct answer is 0.237.