Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't 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 5 questions, find the probability that he will answer all questions correctly? Round your answer to the nearest hundredth.
The easiest way to do this would be to use a binomial probability function table, with n = 5, x = 5, and p = 1/3 (convert the fraction to a decimal).
Look up those values in the table for your probability.
To find the probability that Richard will answer all 5 questions correctly, we need to determine the probability of a single correct answer and raise it to the power of 5, since each question is independent.
Since each question has 3 possible answers, and only 1 is correct, the probability of getting a single question correct is 1/3.
Now, we can calculate the probability using the formula:
Probability of answering all 5 questions correctly = (Probability of a single correct answer) ^ (Number of questions)
Probability of answering all 5 questions correctly = (1/3) ^ 5
Calculating this value gives:
Probability of answering all 5 questions correctly = 0.00411522634
Rounding this value to the nearest hundredth gives:
Probability of answering all 5 questions correctly ≈ 0.00
Therefore, the probability that Richard will answer all questions correctly is approximately 0.00.
To find the probability that Richard will answer all the questions correctly, we need to calculate the probability of getting one question right, and then multiply it by itself for all five questions.
Since there are three answer choices for each question and only one is correct, the probability of guessing the correct answer for a single question is 1/3.
Now, to find the probability of getting all five questions correct, we need to multiply the probability of guessing one question right by itself five times.
So, the probability of answering all questions correctly is (1/3)^5.
Calculating this probability:
(1/3)^5 = 1/243
Rounded to the nearest hundredth, the probability is approximately 0.004
Therefore, the probability that Richard will answer all questions correctly is about 0.004 or 0.4%.