Question

Karolyn is arranging her art project, science project, and math project on her 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 science project is first?

Answers:

three over six
four over six
two over six
one over six

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

It is given that the Karolyn is arranging her art project, science project, and math project on her desk. The tree diagram below shows the sample space.

According to the tree diagram the elements of sample space are

1. art - math - science

2. art - science - math

3. science - art - math

4. science - math - art

5. math - art - science

6. math - science - art

Total number of possible outcomes is 6.

We need to find the probability that the science project is first. So, the favorable outcomes are

1. science - art - math

2. science - math - art

Total number of favorable outcomes is 2.

The probability of arranging the the science project first is

$P=\frac{\text{Favorable outcomes}}{\text{Total possible outcome}}$

$P=\frac{2}{6}$

$P=\frac{1}{2}$

The probability of arranging the the science project first is 2/6 or it can be written as 1/3. Therefore the correct option is 3.

Answer 2

Answer would be two over six