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 32% about 9% about 43.7% about 25% about 46%
Blank 1:
Blank 2:
whats the correct answer
The correct answer for Blank 1 is "about 19%," and the correct answer for Blank 2 is "about 2%."
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?
Let's look at the table and find the cell that corresponds to a purchase price of less than $20,000. We see that there are 100 cars in that category. Now, let's find the cell that corresponds to total repair costs of less than $10,000 within that category. We see that there are 30 cars in that cell.
Therefore, the probability that a car with a purchase price of less than $20,000 has total repair costs of less than $10,000 is 30/100, which simplifies to 0.3 or 30%.
Blank 1: about 30%
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?
Now, let's find the cell that corresponds to total repair costs of less than $10,000. We see that there are 40 cars in that category. Within that category, there are 15 cars with a purchase price of more than $40,000.
Therefore, the probability that a car with total repair costs of less than $10,000 has a purchase price of more than $40,000 is 15/40, which simplifies to 0.375 or 37.5% (rounded to the nearest hundredth).
Blank 2: about 37.5%
To find the probability of an event happening, you need to divide the number of favorable outcomes (cars in the specified category) by the total number of outcomes (total number of cars).
A. To find the probability that the total repair costs were less than $10,000 given a purchase price of less than $20,000, you need to find the number of cars in that specific category. According to the table, there are 24 cars in that category.
Now, find the total number of cars in all categories with a purchase price of less than $20,000. Looking at the table again, you can see that the total number of cars in this group is 126.
To calculate the probability, divide the number of cars with total repair costs less than $10,000 by the total number of cars with a purchase price of less than $20,000:
Probability = Number of cars with total repair costs less than $10,000 / Total number of cars with a purchase price of less than $20,000
Probability = 24 / 126
Simplifying, we get:
Probability ≈ 0.19 (rounded to the nearest hundredth)
So, the probability that a car with a purchase price of less than $20,000 has total repair costs less than $10,000 is about 19%.
Blank 1: about 19%
B. To find the probability of the purchase price being more than $40,000 given total repair costs of less than $10,000, you need to find the number of cars in that specific category. According to the table, there are 24 cars in that category.
Now, find the total number of cars in all categories with total repair costs of less than $10,000. Looking at the table again, you can see that the total number of cars in this group is 55.
To calculate the probability, divide the number of cars with purchase prices more than $40,000 by the total number of cars with total repair costs of less than $10,000:
Probability = Number of cars with purchase prices more than $40,000 / Total number of cars with total repair costs of less than $10,000
Probability = 5 / 55
Simplifying, we get:
Probability ≈ 0.09 (rounded to the nearest hundredth)
So, the probability that a car with total repair costs less than $10,000 has a purchase price more than $40,000 is about 9%.
Blank 2: about 9%
A. From the table, we see that there were a total of 305 cars in the category of purchase price less than $20,000. Of these, 59 had total repair costs less than $10,000. Therefore, the probability is approximately 59/305, which is about 19.34%. So, the answer for Blank 1 is "about 19%."
B. To answer this question, we need to look at the row for total repair costs of less than $10,000. We see that there were a total of 296 cars in this category. Of these, 6 had a purchase price of more than $40,000. Therefore, the probability is approximately 6/296, which is about 2.03%. So, the answer for Blank 2 is "about 2%."