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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?

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    \$\begingroup\$ 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. \$\endgroup\$ – Miniman Sep 4 '16 at 3:11
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    \$\begingroup\$ Note: see this meta for a more thorough explanation. This is a question for a mathematician, not an RPG expert. \$\endgroup\$ – Miniman Sep 4 '16 at 3:27
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    \$\begingroup\$ Can it be migrated? Now that it's been asked, I really want to know... \$\endgroup\$ – SirTechSpec Sep 4 '16 at 3:44
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    \$\begingroup\$ 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? \$\endgroup\$ – Benjamin Lobato Sep 4 '16 at 3:54
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    \$\begingroup\$ 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 =) \$\endgroup\$ – nitsua60 Sep 4 '16 at 3:57