Make a tree diagram to show all the possible sequences of answers for six multiple-choice questions, each with three possible responses. Assuming that you are guessing the answers so that all outcomes listed in the tree are equally likely, what is the probability that you will guess the one sequence that contains all six correct answers? (Round your answer to five decimal places.)

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Answer:

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Based on the information given, the probability that all three are correct will be 0.0000217.

How to calculate the probability

From the information given, there are six multiple-choice questions, each with three possible responses.

If an individual is guessing the answers so that all outcomes listed in the tree are equally likely, the probability that the person will guess the one sequence that contains all six correct answers will be:

A = correct answer = 1/6

B = incorrect answer = 1 - 1/6 = 5/6

The probability of guessing the correct answer will be:

= 1/6 × 1/6 × 1/6 × 1/6 × 1/6 × 1/6

= 0.0000217

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