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As per the rogue feature Expertise, you can choose two skills to double your proficiency bonus in. Obviously this works for active perception checks, but is there anything that says this does or doesn't apply to passive perception?

For example, my Ranger 10 / Rogue 1 has a Wisdom of 17 and a proficiency bonus of +4. Using expertise, this would give me +11 to Perception checks. Therefore, will my Passive Perception be 21?

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Yes, Expertise affects passive Perception checks.

Passive Checks (PHB 175)

Here's how to determine a character's total for a passive check:

10 + all modifiers that normally apply to the check [...]

For example, if a 1st-level character has a Wisdom of 15 and proficiency in Perception, he or she has a passive Wisdom (Perception) score of 14.

Simply put, if you have a WIS mod of +3 and a proficiency bonus of +4 (with proficiency in Perception), your passive Perception score will be 10 + 7, or 17. If you have Expertise in Perception, the +4 is doubled, so you're correct in judging that your passive Perception score will be 21.

Even better, if you're in a context that would grant you advantage on your Perception check, your passive Perception would be no less than 26, thanks to how advantage modifies your passive Perception score:

If the character has advantage on the check, add 5. For disadvantage, subtract 5.

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PHB175 Passive Checks: A passive check is a special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly...

Per the PHB, it does work.

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    \$\begingroup\$ I don't see how the rules you've quoted actually apply to the question asked. Could you please be more explicit and "spell out" what you mean? \$\endgroup\$ – Purple Monkey Aug 22 '17 at 0:44

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