Multiple-choice questions each have 6 possible answers, one of which is correct.
ID: 3375688 • Letter: M
Question
Multiple-choice questions each have 6 possible answers, one of which is correct. Assume that you guess the answers to 3 such questions Use the multiplication rule to find the probability that the first two guesses are wrong and the third is correct. That is, find P(WWC), where C denotes a correct answer and W denotes a wrong answer. (round answer to 2 decimal places) What is the probability of getting exactly one correct answer when 3 guesses are made? (round answer to 2 decimal places) P(exactly one correct answer)- I Points possible: 10 Unlimited attempts Score on last attempt: (0, 0), Score in gradebook: (0, 0), Out of: (5, 5)Explanation / Answer
P(WWC)
The probability that the third question is wrong is 2/3. And we know that the probabilities of the other two being right is 1/3 each, so the probability of just the third question being wrong and the others right is 2/3 × 2/3 × 1/3 = 4/27
4/27 Answer =0.15
2. Since all the answers are independent (the answer to one question has no bearing on the answers to the others), then this is the case with each question, so the chances of guessing all answers correctly is 1/3 × 1/3 × 1/3 = 1/27. Independent choices are linked by multiplication.
To have exactly 1 answers correct, we have to think of which two is wrong: there are 3 questions and any two could be wrong. The probability that the first & second question is wrong is 2/3. And we know that the probabilities of the other one being right is 1/3 each, so the probability of just the first & second question being wrong and the others right is 2/3 × 2/3 × 1/3 = 4/27. But this is just one of the three cases: 1/3 × 2/3 × 2/3 and 2/3 × 1/3 × 2/3 also both equal 4/27 each. So here we add the cases together: 4/27 + 4/27 + 4/27 = 12/27 = 4/9. So the answer of your question is 4/9.
P(Exactly one is correct) = 4/9 = 0.44
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