Question 1 (10 marks) A new car warehouse has 200 cars. It is known that 75% of the cars have air- are manual the rest are automatic. It is also known that 40% of the man conditioning. 8. a. Complete the following table. automatic car manual car car has air-conditioning 76 car does not have air-conditioning Total One car is selected at random, find the probability, giving all answers corre places that the car
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Given that there are 200 cars. It is known that 75% of the cars have air-conditioning.
That is, 200*75%=200*(0.75) =150
So, the remaining 25% of the cars do not have air-conditioning.
That is, 200*25%=200*0.25=50
30% of the cars are manual .
That is, 200*30%=200*0.30=60
The remaining 70% of the cars are automatic.
That is, 200*(70) %=200*(0.70) =140
Also given that 40% of manual cars have air-conditioning.
That is, 60*40%=60*(0.40) =24
That is the remaining 60% of manual cars have does not have air-conditioning.
That is, 60*60%=60*(0.60)= 36
The number of automatic cars having air-conditioning is,
N( cars have air-conditioning with automatic car )
= total number of cars having air-conditioning- N( cars have air-conditioning manual car)
= 150-24
= 126
The number of automatic cars does not having air-conditioning is,
N( cars does not have air-conditioning with automatic car )
= total number of cars does not have air-conditioning- N( cars does not have air-conditioning manual car)
= 50-36
= 14
| Automatic car | manual car | Total | |
| Cars having air-conditioning | 126 | 24 | 150 |
| Cars does not have air-conditioning | 14 | 36 | 50 |
| Total | 140 | 60 | 200 |
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