Question

A taste test asks people from Texas and California which pasta they prefer,

brand A or brand B. This table shows the results.
A person is randomly selected from those tested.
Are being from Texas and preferring brand A independent events? Why or why
not?

Answer 1

Yes, they are independent because P(Texas) ≈ 0.45 and P(Texas/brand A) ≈ 0.45.

Explanation:

We are given that a taste test asks people from Texas and California which pasta they prefer, brand A or brand B. The table is given in the question.

A person is randomly selected from those tested.

And we have find that are being from Texas and preferring brand A independent events or not.

Firstly, we know that these two events will be independent when;

P(Texas) = P(Texas/brand A)

Now, P(Texas) =
`\frac{\text{Number of people from Texas}}{\text{Total number of people}}`

=
`(125)/(275)` ≈ 0.45

Also, P(Texas/brand A) =
`(P(Texas \bigcap Brand A))/(P(Brand A))`

=
`\frac{\text{Number of people from Texas and preferring brand A}}{\text{Number of people preferring brand A}}`

=
`(80)/(176)` ≈ 0.45

Therefore, being from Texas and preferring brand A are independent events because P(Texas) ≈ 0.45 and P(Texas/brand A) ≈ 0.45.