A problem by Spock Weakhypercharge

Level pending

A second grader and a fourth grader playing dodge ball against a third grader and a fifth grader. An xth grader throws a dodge ball and hits a random student from the opposite team every x seconds. When a student gets hit, they instantly swap sides and continue to play as they normally would have, hit cycle uninterrupted. The game ends when all four students are on the same side. What is the probability that the game lasts longer than 5 seconds?

Enter your answer as a decimal.

Clarification: When hit cycle is uninterrupted, this means that each student always when expected. A fifth grader will hit someone every 5, 10, 15, etc. seconds.

[This question is not correct.]


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