Question

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

Answer 1

Answer:

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

Step-by-step 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) =  $\frac{\text{Number of people from Texas}}{\text{Total number of people}}$

                        =  $\frac{125}{275}$  ≈ 0.45

Also,  P(Texas/brand A)  =  $\frac{P(Texas \bigcap Brand A)}{P(Brand A)}$

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

                                        =  $\frac{80}{176}$  ≈ 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.