Question

Aaron Plumbing and Bautista Electrical have both made bids in 50 of the same projects over the years. Aaron was selected for 20 of those projects. Bautista was selected for 15 of the projects, and in 12 of the projects, they both were selected. Use a Venn dia- gram to answer the following questions: a. In what percentage of the projects was Bautista selected, but Aaron was not

Answer 1

In 6% of the projects was Bautista selected, but Aaron was not

Explanation:

Building the Venn diagram, I am going to say that:

-A is the number of projects that Aaron was selected.

-B is the number of projects that Bautista was selected.

We have that:

`A = a + (A \cap B)`

In which a is the number of projects that only Aaron was selected and
`A \cap B` is the number of projects that both were selected.

By the same logic, we also have that:

`B = b + (A \cap B)`

In what percentage of the projects was Bautista selected, but Aaron was not

There were b projects that Bautista was selected and Aaron not. The total number projects is 50. So this percentage is b/50.

We start finding the values from the intersection.

12 of the projects, they both were selected. This means that
`A \cap B = 12`

Bautista was selected for 15 of the projects, so
`B = 15`

`B = b + (A \cap B)`

`15 = b + 12`

`b = 3`

--------

`P = (3)/(50) = 0.06`.

In 6% of the projects was Bautista selected, but Aaron was not