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Question
In a sample of 40 vehicles, 18 are red, 6 are trucks, of which 2 are red. Suppose that a randomly selected vehicle is red. What is the probability it is a truck?
Solution
There are 40 vehicles
∴ n(S) =40
Let A ≡ the event that vehicle is red
B ≡ the event that vehicle is a truck
We are given that vehicle is red
∴ our sample space reduces to A for which n(A) = 18
Since there are two trucks which are red,
n(A ∩ B) = 2
Probability that vehicle is a truck given that vehicle is red
= `"P"("B"//"A")`
= `("n"("A" ∩ "B"))/("n"("A")`
= `2/18`
= `1/9`
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