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 32% about 20% about 43.7% about 9% about 25% about 46%
Blank 1:
Blank 2:
A. about 20%
B. about 9%
A. According to the table, if the purchase price of a car was less than $20,000, the probability that its total repair costs were less than $10,000 is about 46%.
B. If a car had total repair costs of less than $10,000, the probability that its purchase price was more than $40,000 is about 32%.
A. According to the table, if the purchase price of a car was less than $20,000, the number of cars in that category is 13+7+14=34.
Out of these 34 cars, the number of cars with total repair costs less than $10,000 is 5+3+7=15.
Therefore, the probability that a car with a purchase price of less than $20,000 has total repair costs less than $10,000 is 15/34, which is about 44.1%.
Blank 1: about 44.1%
B. If a car had total repair costs of less than $10,000, the number of cars in that category is 5+3+7+1+1+2+4+2=25.
Out of these 25 cars, the number of cars with a purchase price of more than $40,000 is 4.
Therefore, the probability that a car with total repair costs less than $10,000 has a purchase price of more than $40,000 is 4/25, which is about 16%.
Blank 2: about 16%
To answer these questions, we need to use the information given in the table.
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 look at the intersection of the two categories. From the table, we can see that the number of cars in the category where purchase price is less than $20,000 and total repair costs are less than $10,000 is 10. Therefore, the probability can be calculated as the number of cars in that category divided by the total number of cars with purchase price less than $20,000:
Probability = (number of cars with purchase price < $20,000 and total repair costs < $10,000) / (total number of cars with purchase price < $20,000)
Plugging in the values, we have:
Probability = 10 / 50 = 1 / 5 = 0.2
So, 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 20%.
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 look at the intersection of the two categories. From the table, we can see that the number of cars in the category where total repair costs are less than $10,000 and purchase price is more than $40,000 is 6. Therefore, the probability can be calculated as the number of cars in that category divided by the total number of cars with total repair costs less than $10,000:
Probability = (number of cars with total repair costs < $10,000 and purchase price > $40,000) / (total number of cars with total repair costs < $10,000)
Plugging in the values, we have:
Probability = 6 / 50 = 0.12
So, 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 0.12 or 12%.