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Cumulative Probability

Suppose the probabilities that a new car battery functions
For at least 20, 000km is 0.8
For at least 40, 000km is 0.5,
For at least 60, 000km is 0.1.

(i) Given that the battery still works at 20, 000 km, what is the probability that it lasts for at least another 20, 000km?
(ii) Given that the battery still works at 20, 000 km, what is the probability it lasts for at least another 40, 000km?

Solution Preview

We can say that
P(40,000 km) = P(first 20,000 km) * P(another 20,000 km given it lasted the first 20,000)

Therefore ...

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