You may remember the aliens Arglbzz and Brthflum from Challenge 441, where they were racing against Clonk.

This time Arglbzz and Brthflum are playing a game of alien archery. In each round, the player closest to the centre of the target gets a point, but if both players miss the target then neither of them wins a point.

It so happens that in each round, Arglbzz has probability 0.5 of being closest to the target, while Brthflum has probability 0.3 of being closest to the target.

If they play a 7-round game, what is the probability that someone wins? (In other words, the probability that the game is not a draw.)

Note: for this problem, unlike most WMC problems, I would encourage use of a calculator to evaluate your answer. You should still include full working with your solution!