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Answer:
a) Probability that vehicle is Light Truck is 0.69
b) Probability that vehicle is imported car is 0.08 or 8%.
Step-by-step explanation:
Part a)
Event that vehicle is a car is given by A. Since, the vehicles can only be classified as cars or light trucks, the event that a vehicle will be light truck will be compliment of A.
i.e. Event that vehicle is a Light Truck =
It is given that in recent year 69% of vehicles sold were light trucks, 78% were domestic, and 55% were domestic light trucks.
So, from here we can say that, if a vehicle is randomly selected from all the vehicles the probability that it would be a light truck will be:
P(Vehicle will be Light Truck) = P() = 69% = 0.69
Part b)
Event that vehicle is imported is given by B. We need to find the probability the a randomly chosen vehicle is an imported car i.e. we have to find probability of occurrence of events A and B together, which will be denoted as: P(A and B)
Since, P() = 69% = 0.69
P(A) = 1 - P() = 1 - 0.69 = 0.31
It is also given that 78% of vehicles were domestic. This means, the percentage/probability of imported vehicles is:
P(B) = 1 - 0.78 = 0.22
55% of vehicles were domestic light trucks. This can be expressed as:
, the compliment of this event will give us P(A or B).
i.e.
P(A or B) = 1 - = 1 - 0.55 = 0.45
According to the addition rule of probabilities:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the calculated values gives us:
0.45 = 0.31 + 0.22 - P(A and B)
P(A and B) = 0.08
This means, the probability that vehicle is imported car is 0.08 or 8%.