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schepotkina [342]
3 years ago
15

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

Mathematics
1 answer:
melamori03 [73]3 years ago
6 0

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.        

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