Question 13 (2 points)
A consumer magazine investigated the relationship between new car purchase price and total repair costs over a 10-year period. The data are summarized in the table below. Each cell in the table shows the number of cars in that category.
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A. According to the table, if the purchase price of a car was less than $20,000, what is the probability that its total repair costs were less than $10,000?
B. If a car had total repair costs of less than $10,000, what is the probability that its purchase price was more than $40,000? Express your answer as a decimal rounded to the nearest hundredth.
Word Bank:
about 20%
about 9%
about 43.7%
about 32%
about 46%
about 25%
Blank 1:
Blank 2:
A. Blank 1: about 25%
B. Blank 2: about 9.26%
Is that the answer
Yes, that is the answer.
9.26 isn’t an answer
Sorry for the confusion. The answer for Blank 2 is approximately 9%.
A. To find the probability that a car's total repair costs were less than $10,000 given that its purchase price was less than $20,000, we need to use conditional probability.
First, we need to find the total number of cars that have a purchase price less than $20,000, which is the sum of the values in the first row of the table: 10 + 40 + 20 + 30 + 10 = 110.
Next, we need to find the number of cars that have both a purchase price less than $20,000 and total repair costs less than $10,000. We look for the intersection of the cell representing purchase price less than $20,000 and total repair costs less than $10,000, which is the cell in the second row and first column of the table. The value in that cell is 10.
Now, we can calculate the probability by dividing the number of cars with both conditions (10) by the total number of cars with a purchase price less than $20,000 (110).
Probability = 10/110 = 1/11 ≈ 0.0909
Therefore, the probability that a car's total repair costs were less than $10,000 given that its purchase price was less than $20,000 is about 9%.
Blank 1: about 9%
B. To find the probability that a car's purchase price was more than $40,000 given that its total repair costs were less than $10,000, we need to use conditional probability again.
First, we need to find the total number of cars that have total repair costs less than $10,000, which is the sum of the values in the first column of the table: 10 + 30 + 20 + 20 + 30 = 110.
Next, we need to find the number of cars that have both total repair costs less than $10,000 and a purchase price more than $40,000. We look for the intersection of the cell representing total repair costs less than $10,000 and purchase price more than $40,000, which is the cell in the first row and fifth column of the table. The value in that cell is 30.
Now, we can calculate the probability by dividing the number of cars with both conditions (30) by the total number of cars with total repair costs less than $10,000 (110).
Probability = 30/110 ≈ 0.2727
Therefore, the probability that a car's purchase price was more than $40,000 given that its total repair costs were less than $10,000 is about 27.27%.
Blank 2: about 27.27%