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a taste test asks people from Texas and California which pasta they prefer, brand A or brand B. this table shows the results

a taste test asks people from Texas and California which pasta they prefer brand A or brand B this table shows the results class=

Respuesta :

frika

Answer:

D.

Step-by-step explanation:

Two events A and B are independent when

[tex]P(A|B)=P(A),[/tex]

where [tex]P(A|B)[/tex] is the probability that event A occurs given that event B has occured.

A = randomly selected person is from California

B = randomly selected person preferred brand A

A|B =  being a person from California and preferring brand A.

Hence,

[tex]P(A)=\dfrac{150}{275}=\dfrac{6}{11}\approx 0.55\\ \\P(B)=\dfrac{176}{275}=\dfrac{16}{25}=0.64\\ \\P(A|B)=\dfrac{96}{176}=\dfrac{6}{11}\approx 0.55[/tex]

Since  [tex]P(A)=P(A|B),[/tex] events are independent.

luisejr77

Answer: Option D

Step-by-step explanation:

First we assign names to events:

Event C: The selected people are from California

Event A: The selected person prefers the A mark

Now notice in the table that the total number of people is: 275.

Then, the number of people who prefer the A mark is: 176

The number of people who are from California is: 150

The number of people in California who prefer the A brand is: 96

Then we have that:

[tex]P(C)=\frac{150}{275}=\frac{6}{11}=0.55[/tex]

[tex]P(A)=\frac{176}{275}=\frac{16}{25}[/tex]

[tex]P (C\ and\ A) = \frac{96}{275}=0.3491[/tex]

Then:

[tex]P(C|A)=\frac{P(C\ and\ A)}{P(A)}\\\\P(C|A)=\frac{\frac{96}{275}}{\frac{16}{25}}=\frac{6}{11}=0.55[/tex]

By definition two events C and A are independent if and only if:

[tex]P (C\ and\ A) = P (A)*P (C)[/tex]

Then, if A and C are independent events, it must be fulfilled that:

[tex]P(C|A)=\frac{P(A)*P(C)}{P(A)}\\\\P(C|A)=P(C)[/tex]

Note that [tex]P (C) = 0.55[/tex] and [tex]P (C | A) = 0.55[/tex]

So:

[tex]P (C | A) = P (C)[/tex]

Therefore the events are independent and  [tex]P (C) =P (C | A) = 0.55[/tex]

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