Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability (resit) / 7 / b / iii / Solution

Let $D$ be the number of days up to and including the first breakdown, and $M$ the event of a morning first breakdown. For $d=1,2,\dots$, conditional probability givesThusThis geometric distribution counts the day on which the first breakdown occurs. Its parameter is the probability of at least one breakdown during a day, rather than the morning breakdown probability $\alpha$ alone.