Imagine a probe in space. Argon gas can be fired from the probes fuel tanks to propel the probe. Discuss whether conservation of momentum applies and whether the speed of the probe increases.

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Conservation of momentum always applies (1) in physical situations, and is considered one of the basic building blocks of physics. So therefore when Argon is fired from the tank, in order for the net change in momentum to be zero, then the probe and Argon most move in opposite directions (1). Following on from this it also stand to reason that the change in momentum of the probe must be the same as that of the Argon (1).
Another law in physics is the conservation of energy, of which energy must always be conserved (1). Energy must be put into the system, of the probe and Argon, to fire the Argon from the probe. This energy can then be converted to kinetic energy. Therefore the speed of the Argon and the probe can increase. (You can also state here other ways energy can be converted, but not sound as sound doesn't travel in space)