Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 207 / 4 / a / Solution

The risk sets at the six event times are $(7,6,5,3,2,1)$, each with one event: the censoring between $t_3$ and $t_4$ removes the seventh individual before the fourth event. Thus the survivor estimate after the fifth event isConditional on reaching $t_4$, the event mass at $t_4$ is $1/3$, that at $t_5$ is $(2/3)(1/2)$, and that at $t_6$ is $(2/3)(1/2)(1)$. Hence the conditional event probabilities are