question 6 of 10\na taste test asks people from texas and california which pasta they prefer, brand a or…
question 6 of 10\na taste test asks people from texas and california which pasta they prefer, brand a or brand b. this table shows the results.\n| | brand a | brand b | total |\n|--|--|--|--|\n| texas | 80 | 45 | 125 |\n| california | 90 | 60 | 150 |\n| total | 170 | 105 | 275 |\na person is randomly selected from those tested.\nwhat is the probability that the person is from texas, given that the person prefers brand b? round your answer to two decimal places.\na. 0.38\nb. 0.45\nc. 0.36\nd. 0.43
Answer
Explanation:
Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequency, if $A$ is the event that a person is from Texas and $B$ is the event that a person prefers brand B, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of people who are from Texas and prefer brand B, and $n(B)$ is the number of people who prefer brand B.
Step2: Identify the relevant values from the table
From the table, the number of people who are from Texas and prefer brand B, $n(A\cap B) = 45$. The number of people who prefer brand B, $n(B)=105$.
Step3: Calculate the probability
$P(A|B)=\frac{45}{105}\approx0.43$
Answer:
D. 0.43