Instead of thinking of day length of vacations, because I think that is confusing, instead think of it like this: Therefore:Īll the vacations seem equally fun to you, so you just decide to pick one of the three at random. Since these events are independent (the dice do not influence each other), we can sum the probabilities. There are two possiblities for 3, 1 and 2, and 2 and 1. There is only one combination that gives us 2, so P(2) = 1/36. Probability gets very complex very quickly when you start asking about probabilities beyond single events.Īn easier way would be to use the complement: So when you bring inequalities into the mix, you are actually asking about every single possible outcome above the one you want! Each of these probability events must be individually calculated and summed. ![]() P(A + B) = P(4 OR 5 OR 6 OR 7 OR 8 OR 9 OR 10 OR 11 OR 12) This is a trickier question to answer than you might think, since from a mathematical perspective, here is what you are really asking: ![]() So mathematically, you want this: P(A + B) >= 4. For example, there are many ways to roll 7, but only one combination will roll 12. A and B are discrete random variables with outcomes S = Our sample space contains 36 possible outcomes, but not all of those outcomes are equally likely. Let P(A) be the probability of the first die roll, and P(B) be the second die roll. What you're asking for is really the combination of several probability events. ![]() The hard answer is that there really isn't one catch-all plug-and-play formula for what you want.
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