I am slowly learning the basics of probability theory. I have realized that learning theorems on continuity of probability and rigorous proofs is one thing, but solving problems is something totally different
Let X represent the lifetime, rounded up to an integer number of years, of a certain car battery.Suppose that the pmf of X is given by if and otherwise.
(i)Find the probability, P [X > 3], that a three year old battery is still working.
(ii) Given that the battery is still working after ﬁve years, what is the conditional probability that the battery will still be working three years later? (i.e. what is P [X > 8|X > 5]?)
(i)I thought this was straightforward and noted that it is a discrete distribution. So
(ii) Here I am stumped. The lifetime of the battery has an equally likely chance of failing from 3rd year to 7th year. How can the battery still work at around the 8th year?!
I have most likely misunderstood the problem. Moreover this problem is to motivate "geometric" distribution!
Any help appreciated