Like. I know they are different and that one is less likely. But could someone explain this in a way that I can explain it to my partner? I know it is true but cannot remember anything about why and how to explain my point.
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It depends on the situation. If you’re talking about OR probabilities (i.e. P(A or B)) and the events are mutually exclusive, then then we’d just add the individual probabilities and get 0.07+0.07… 0.07=10*0.07=0.7. But if the events aren’t mutually exclusive (i.e. more than one of them can happen) we have to subtract the compound probability. That is, the general rule for OR probabilities is P(A or B) = P(A)+P(B)-P(A and B). (If you wanna know why that’s the formula, Google “venn diagrams for or probability”; I’d post some diagrams here, but I’m on mobile).
On the other hand, if we’re talking about AND probabilities, they don’t combine by addition. If the events are independent (i.e. knowing that one event occurred or didn’t doesn’t effect the probability of the other events), then P(A and B) = P(A)•P(B). More generally, P(A and B)=P(A)•P(B|A)=P(B)P(A|B).
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