solve the math problem?
Multiple-choice questions on a test each have 4 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.
a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the last 3 guesses are correct. That is, find P(WWCCC), where C denotes a correct answer and W denotes a wrong answer.
b. Make a complete list of the different possible arrangements of 2 wrong answers and 3 correct answers, then find the probability for each entry in the list.
c. Based on the preceding results, what is the probability of getting exactly 3 correct answers when 5 guesses are made?
- TomVLv 74 months agoFavorite Answer
Probability of a correct answer on any given question = 1/4
Probability of a wrong answer on any given question = 3/4
a) P(WWCCC) = (3/4)(3/4)(1/4)(1/4)(1/4) = 3²/4⁵ = 9/1024 ≈ 0.879%
b) There are 10 possible arrangements of 2 wrong and 3 correct answers. All of them have the same probability, 3²/4⁵ = 9/1024
c) Since there are 10 possible outcomes, each of which have the same probability of occurring, the probability of achieving any one of those 10 outcomes is the sum of their individual probabilities, 10*(9/1024) = 90/1024 = 45/512 ≈ 8.79%