# 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? - Mathematics and Statistics

Sum

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

Concept: Multiplication Theorem on Probability
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