At a parking lot there are 1640 vehicles, 160 of which are trucks, 830 are small cars and the remainder are motorcycles.
Find the probability of:
a. motorcycles leaving first.
b. a truck leaving first.
c. a car leaving third if either a lorry or van had left first.
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Explanation:
a. To find the probability of a motorcycle leaving first, we need to know the total number of motorcycles in the parking lot. We can find this by subtracting the number of trucks and small cars from the total number of vehicles:
Total number of motorcycles = Total number of vehicles - Number of trucks - Number of small cars
Total number of motorcycles = 1640 - 160 - 830
Total number of motorcycles = 650
So the probability of a motorcycle leaving first is:
P(motorcycle leaving first) = Number of motorcycles / Total number of vehicles
P(motorcycle leaving first) = 650 / 1640
P(motorcycle leaving first) = 0.396
b. The probability of a truck leaving first is simply the number of trucks divided by the total number of vehicles:
P(truck leaving first) = Number of trucks / Total number of vehicles
P(truck leaving first) = 160 / 1640
P(truck leaving first) = 0.098
c. If either a lorry or van had left first, there would be 1639 vehicles left in the parking lot, and we would need to choose a car for the third vehicle to leave. The probability of choosing a small car for the third vehicle to leave would be:
P(choosing a small car | lorry or van left first) = Number of small cars / (Total number of vehicles - 1)
P(choosing a small car | lorry or van left first) = 830 / 1639
P(choosing a small car | lorry or van left first) = 0.506
Note that we divide by (Total number of vehicles - 1) because one vehicle has already left the parking lot.