Q16Single correct3 Marks7 Jul 2024

Suppose that the number of miles that a car can run before its battery wears out is exponentially distributed, with an average value of $10000$ miles. If you desire to take a $5000$-mile trip, what is the probability that you will be able to complete the trip without replacing the car battery?

A

$\frac{1}{10000}\exp\left(-\frac{5000}{10000}\right)$

B

$10000\exp(-5000\times10000)$

C

$1-\exp\left(-\frac{5000}{10000}\right)$

D

$\exp\left(-\frac{5000}{10000}\right)$