Lloyd is arranging his science project, math project, and art project on his desk. the tree diagram below shows the sample space. a tree diagram is shown. the first three choices are art, science, and math. from art, one branch is math, science and the other branch is science, math. from science, one branch is art, math and the other branch is math, art. from math, one branch is art, science and the other branch is science, art. based on the tree diagram, what is the probability that the projects are in order of art, math, science? one over six two over six three over six four over six

The tree diagram is constructed and attached below in the image.

First we have to make a choice out of 3 subjects, so the probability of choosing art as the first subject is 1/3.

Once we have chosen art as the first subject, we have two choices. So the probability of choosing each option now is 1/2. Thus, the probability of choosing math, science is 1/2.

The probability of choosing the projects in order of art, math, science = 1/3 x 1/2 = 1/6

Therefore, the probability that the projects are in order of art, math, science is 1/6 (one over 6). So first option gives the correct answer.

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