Chance Activation

A group has found an item (an artifact, some piece of supposedly incomprehensible technology, etc.). The group, most likely including the smart guy, starts discussing how it will take quite a bit of time and research to discover the item's purpose and/or how to use it. Meanwhile, another person in the group (often The Hero, but not necessarily) is fiddling around with the item, and unlocks/activates/arms/whatevers the device, interrupting and possibly upsetting the others in the group.

In cases where the method of using the item in question is discovered by someone of lesser intelligence, this trope becomes a specific example of Too Dumb to Fool.

Note that sometimes the activation isn't necessarily a good thing.

Related to Cut the Juice and Cutting the Knot, with the exception that the characters here are not necessarily trying to solve an immediate problem.

Compare Shaggy Search Technique, where the person or group is actively trying to solve whatever puzzle is present, inadvertently finding a solution through dumb luck. The main difference between these tropes is a matter of intent; Shaggy searches begin intentionally, while a chance activation is just someone fiddling with a Plot Device and it "working".

Examples of Chance Activation include:

Film

Occurs in Treasure Planet, after the Benbow Inn has been burnt down and the Hawkinses are staying with Dr. Doppler. The good doctor is explaining that he has no clue of function of the "odd little sphere" which Jim now possesses. Cue Jim fiddling around with the sphere and unlocking it, thereby discovering its function; a map containing the location of the legendary Treasure Planet.
The Air element stone in The Fifth Element is opened by pure dumb luck (the trainee priest sighing at it in frustration), providing the key clue needed to open the three others.
The gun over the bar at the Winchester in Shaun of the Dead. Slightly different, in that they knew how to use it, they just thought it wouldn't work. And then it goes off in Shaun's hands.

Ed: I fucking knew it!

In the Green Lantern movie, Hal has been given a magic ring and a magic lantern by the dying Aben Sur, but no instructions on how to use either, nor what the Green Lantern oath is supposed to be. He fools around with both for the better part of an afternoon, offering a number of possible activation phrases (including "By the power of Greyskull!" and |"To infinity and beyond!") until he gets the connection just so and the ring and lantern take over for him.

Literature

In Five Children and It by E. Nesbit, while everyone tries to figure out how to open the door, the baby is playing with the lock. The door swings open.
In The Cloakmaster Cycle Teldin was not amused to know some possible results of Tinker Gnomes' "thingfinder" malfunctions and when it got damaged he ordered another guy to quietly get rid of it. Thus the trinket ended up in a jettison (sort of catapult used as Short-Range Shotgun) and eventually was fired at an enemy. On impact, Hilarity Ensues.
In the Discworld book Thud!, It's revealed that this is how Mad Artist Methodia Rascal activated (and was subsequently driven even crazier by) the dwarfs' talking Cube. As he thought he was a chicken, the noises he would make (Awk! Awk!) happened to sound like the Dwarfish word that turned it on.

Video Games

At the end of the very first mission of Mass Effect, Shepard's squadmate (Ashley if Shepard is male, Kaiden if Shepard is female) activates the beacon they've been looking for by simply walking too close to it.

Western Animation

In one episode of The Simpsons, after much hilarity ensuing, Homer drops a priceless Egyptian artifact, which is then discovered to be a music box which nobody knew about. Lisa decides that it's best to keep it just between them.
In Batman Vs Dracula, The Penguin just happens to cut his hand on his umbrella-sword, giving Dracula the drop of blood he needs to rise from the grave.