suppose that the total number of thousands of miles that a car can be driven before it would need to be junked is an exponential random variable with parameter 1 20 . if alice purchases a used car that has already been driven for 10,000 miles, what is the probability that she would get at least 20,000 additional miles out of it?



Answer :

The probability that she would get at least 20,000 additional miles out of it is 0.3678.

Let X denote the total number of thousands of miles that the car is driven before it needs to be junked. We want to compute P({X≥30} | {X≥10}).

Assuming X is an exponential random variable with parameter 1/20, we have

P{X≥30} = [tex]e^{-3/2}[/tex]

P{X≥10} = [tex]e^{-1/2}[/tex]

P({X≥30} | {X≥10}) = P{X≥30} / P{X≥10}  

                            =  [tex]e^{-3/2}[/tex] /  [tex]e^{-1/2}[/tex]

                            = [tex]e^{-1}[/tex]

                            ≈ 0.3678

Hence, the probability is 0.3678.

To learn more about probability here:

https://brainly.com/question/11234923

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