IIM-K (BMSAT) 2025 (QA) PYQs

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

The probability that a randomly chosen factor of $10^{19}$ is a multiple of $10^{15}$ is

There is a 4-in-5 chance that A can complete the marathon. There is a 5-in-8 chance that B can't complete the marathon, which is independent of A's performance. What is the probability that both A and B end up completing?