Question

Make a tree diagram to show all the possible sequences of answers for four multiple-choice questions, each with five 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 four correct answers?

Answer 1

Answer: Here's a tree diagram that shows all the possible sequences of answers for four multiple-choice questions, each with five possible responses:

/-- A -- A -- A -- A

/

/ /-- A -- A -- A -- B

/ /-- A -- A -- B -- A

/ /-- A -- B -- A -- A

/ /-- B -- A -- A -- A

/ /

/ / /-- A -- A -- B -- B

/ / /-- A -- B -- A -- B

/ / /-- A -- B -- B -- A

/ / /-- B -- A -- A -- B

/ / /-- B -- A -- B -- A

/ / /-- B -- B -- A -- A

/

/ /-- A -- B -- B -- B

/ /-- B -- A -- B -- B

/ /-- B -- B -- A -- B

/ /-- B -- B -- B -- A

/

/ /-- A -- B -- B -- B

/ /-- B -- A -- B -- B

/-- B -- B -- A -- B

/-- B -- B -- B -- A

Each branch in the tree represents the guess for one of the questions, and the letters A and B represent the possible answers. There are 5 branches coming out of each node in the tree because there are 5 possible answers for each question.

To find the probability of guessing the one sequence that contains all four correct answers, we multiply the probabilities of following the path A-A-A-A:

P(A-A-A-A) = (1/5) * (1/5) * (1/5) * (1/5) = 1/625

Therefore, the probability of guessing the one sequence that contains all four correct answers is 1/625 or about 0.16%.

Explanation: