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.

I think it's something like:

6/120 or 1/20 that it will have mileage and the air conditioner.

60/200 or 3/10 have a working air conditioner.

Can someone help me with the rest and check it? Thanks!

.60 less than 75000 .40 more

.65 air condition .30 air

.60 times .65 low and air

.65 + .30 have working air

Is my probability correct?

Sure! Let's break down the problem step by step and tackle each part.

a) To create a table or tree diagram, you can start by organizing the given data into categories. Let's use 'Low Mileage' and 'Working Air Conditioner' as our categories.

| Low Mileage | High Mileage
-------------------------------------------------
Air Conditioner | |
Working | |
Not Working | |

Now, fill in the known values based on the given information. From the problem statement, 60% of the 200 cars have low mileage, so we can calculate that to be:

Low Mileage = 60% of 200 = (60/100) * 200 = 120

Since we now know the number of low mileage cars, we can proceed to determine the number of cars with a working air conditioner. The problem states that 65% of the low mileage cars have a working air conditioner, so:

Low Mileage and Working Air Conditioner = 65% of 120 = (65/100) * 120 = 78

Next, we know that the remaining cars have high mileage (200 - 120 = 80). Among these high mileage cars, only 30% have a working air conditioner, so:

High Mileage and Working Air Conditioner = 30% of 80 = (30/100) * 80 = 24

Fill in the values in the table:

| Low Mileage | High Mileage
-------------------------------------------------
Air Conditioner | 78 | 24
Working | |
Not Working | |

b) The probability that a car looked at has low mileage and a working air conditioner can be calculated by dividing the number of cars that satisfy both conditions (78) by the total number of cars looked at (200).

Probability = Number of cars with low mileage and working air conditioner / Total number of cars looked at

Probability = 78 / 200 = 0.39 or 39%

So, the probability is 39% or 0.39.

c) The probability that a car has a working air conditioner can be calculated by dividing the total number of cars with a working air conditioner (78 + 24) by the total number of cars looked at (200).

Probability = Number of cars with a working air conditioner / Total number of cars looked at

Probability = (78 + 24) / 200 = 102 / 200 = 0.51 or 51%

So, the probability is 51% or 0.51.

I hope this clarifies the problem for you! Let me know if you have any further questions or need additional assistance.