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In Dungeons and Dragons fifth edition, group ability checks are done with everyone in the group making the ability check. If at least half the group succeeds, the whole group succeeds. Otherwise, the group fails.

Let's say in a group of six players, two have a 55% chance to pass the check. Four others have a 60% chance. What is the probability that at least three will pass the check?

user17995
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Benjamin Lobato
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    I'm voting to close this question as off-topic because it's a basic probability question where the RPG context makes no difference whatsoever. – Miniman Sep 04 '16 at 03:11
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    Note: see this meta for a more thorough explanation. This is a question for a mathematician, not an RPG expert. – Miniman Sep 04 '16 at 03:27
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    Can it be migrated? Now that it's been asked, I really want to know... – SirTechSpec Sep 04 '16 at 03:44
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    I was worried that this was more of a math question than an RPG question, but one of the top voted 5e questions on here is very similar: How does rolling two dice and taking the highest affect the average outcome? – Benjamin Lobato Sep 04 '16 at 03:54
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    I'll admit, I don't see much daylight between this question and What is the probability of surviving my death saves? In fact, the reason I'd copied the link was to tell @SirTechSpec that really understanding the answer to the death-saves question would give one enough to work out the answer to this one. There are some subtleties which, of course, are left as exercises for the reader =) – nitsua60 Sep 04 '16 at 03:57
  • @nitsua60 I'd really like to see how we can solve that specific question using probabilities like you did in the link you provide (and, why not, how can it be sorted out in Anydice?) – Meta4ic Sep 04 '16 at 11:40
  • @Meta4ic If this gets reopened I'm happy to write up an answer. I'd try to show--through this specific problem--how one could calculate the general case so that in the likely circumstance that this exact set of probabilities isn't your use-case the answer would still be instructive. (Or ping me in [chat] any time. I like talking math!) – nitsua60 Sep 04 '16 at 12:00
  • The difference is that neither understanding the description of the problem nor answering it requires RPG knowledge (let alone expertise). It's like those math problems where trains leave certain cities at certain times and speeds—it's not a question for railway experts, just math experts. No RPG expertise is called on by this question. – SevenSidedDie Sep 04 '16 at 13:21
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    @SevenSidedDie What you say is true, but knowing how to estimate the odds of group check successes (over odds of individual checks, for instance) might help one understand better what each option provides (or yields to the other). If I may use your metaphor, i'd say that railway experts may rely on math experts to decide where they're gonna build their siding tracks. – Meta4ic Sep 04 '16 at 18:45
  • @Meta4ic Exactly. That's why it's off topic for this Stack, but could be asked on [math.se] SE, where the math experts are, per our meta on this kind of thing. – SevenSidedDie Sep 04 '16 at 18:46

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