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) = [tex]\frac{\text{Number of people from Texas}}{\text{Total number of people}}[/tex]
= [tex]\frac{125}{275}[/tex] ≈ 0.45
Also, P(Texas/brand A) = [tex]\frac{P(Texas \bigcap Brand A)}{P(Brand A)}[/tex]
= [tex]\frac{\text{Number of people from Texas and preferring brand A}}{\text{Number of people preferring brand A}}[/tex]
= [tex]\frac{80}{176}[/tex] ≈ 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.
