User:Nsh/STEP-II-Stats-Question

A mens endurance competition has an unlimited number of rounds. In each round, a competitor has, independently, a probability /p/ or making it through the round; otherwise, he fails the round. Once a competitor fails a round, he drops out of the competition; before he drops out, he takes part in every round. The grand prize is awarded to any competitor who makes it though a round which _all_the_other_remaining_competitors_fail; if all the remaining competitors fail at the same round the grand prize is not awarded.

If the competition begins with three competitors, find the probability that:
(i) all three drop out in the same round;
(ii) two of them drop out in round /r/ (with /r/ >= 2) and the third in an earlier round;
(iii) the grand prize is awarded.


You can edit this page and use <math></math> tags Guide for formula (TeX markup, quite easy to learn)