Try drawing out a venn diagram. Let G be one circle, and H be another cricle. The region of overlap in the area where both occur. The quantity A is just asking for the probability where only G or only H will occur.
In essence that will reduce to the area in circle G minus the common area (To get the area of only G) and the area in circle H minus the common area (To get the area of only H). Notice how you had to subtract the common area twice? That would be my reasoning.
Thanks, gotcha. I also came to a conclusion using the formula, in case of counting either G or H or Both, we subtract the product only once to cut off the double counting of the commonly shared place, so there exists still a commonly share place which we are addressing as both. But Quantity A is asking for “not both”, so we have to cut that product again to totally get rid of the part, thus ultimately we are subtracting that twice.
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