Taylor wants a used car, he would like for it to have a working air conditioner and less than 75,000 miles on it . Of the 200 cars ads he looked at, 60% have less than 75,000 miles. Of these low-mileage cars 65% had a working air conditioner. Of the cars with more than 75,000 miles, only 30% had a working air conditioner.
a) Make a table or tree diagram to show the data.
b) What is the probability that a car looked at has low mileage and a working air conditioner.
c) What is the probability that a car has a working air conditioner.
Help! I only have 2 hours until this is due!
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As for my answers, for A I made a small chart with each detail: Working AC, Less Than 75,000 miles and both.
B: 130/200 or 13/20
C: 13/20 + 16/20 = 19/20
a) To create a table or tree diagram, we need to organize the given data into a clear format:
Less than 75,000 miles | More than 75,000 miles
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Working AC | ? |
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Non-working AC | ? |
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We can fill out the known probabilities in the table:
Less than 75,000 miles | More than 75,000 miles
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Working AC | 0.60 | 0.30
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Non-working AC | ? | ?
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b) The probability that a car looked at has low mileage and a working air conditioner is calculated by multiplying the probability of having low mileage by the probability of having a working AC among low-mileage cars. So, the probability is:
P(Low mileage and Working AC) = P(Less than 75,000 miles) * P(Working AC | Low mileage)
= 0.60 * 0.65
= 0.39
Therefore, there is a 39% chance that a car looked at has low mileage and a working air conditioner.
c) To find the probability that a car has a working air conditioner, we need to consider both low-mileage and high-mileage cars. The probability is calculated by adding the product of individual probabilities in each category:
P(Working AC) = P(Low mileage and Working AC) + P(More than 75,000 miles and Working AC)
= 0.39 + (0.40 * 0.30)
= 0.39 + 0.12
= 0.51
Therefore, there is a 51% chance that a car looked at has a working air conditioner.
Now you have the table, and the probabilities required to answer parts b) and c). Good luck with your assignment!