I'm currently writing a dissertation on piracy in the late medieval Mediterranean (late 13th and early 14th century). No time to write a lengthy response right now, but this is the first time I've seen a question on /askhistorians that's straight up my alley. So I must respond!

From the 1000+ documents I'm working with, I can say that piracy was very common during this period. However, the sheer volume of trade going on at the time meant that most voyages went unharmed.

I can't put a number on it myself--not yet--but I can throw out some mildly-educated estimate and say that from the years 1291-1327, corresponding to the reign of James II, I've located nearly 1000 records corresponding to pirate attacks. Some of them overlap, of course. But these are only for the archives in Barcelona and correspond primarily to merchants from that city. And I haven't gone through anything resembling the "entirety" of the documentation just in Barcelona from that period.

But Henri Bresc, writing about Sicily during this era, estimated that perhaps 30% or more voyages were taken by pirates. This was supposed to be exceptional and demonstrate how crazy the seas around Sicily were during this time. His guesstimate has been cited and repeated by other historians.

Commendas, the contracts used in the medieval maritime trade, often included clauses for what would happen in cases of piracy, as would peace or trade treaties between different principalities. Both of these indicate that it was a pretty common problem. Later in the 14th and early 15th cetury, the Crown of Aragon began regulating trade much more heavily, requiring that ships be armed and that valuable shipments go with Galley escorts, indicating that the danger of pirates must have increased some over the course of that era.

Regardless of numbers, piracy was a constant fear in the minds of merchants and coastal peoples. Most piracy during my period was mere robbery--homocide was actually fairly uncommon--but the effects of a single pirate attack could ruin your career as a merchant and bankrupt your family. If you were Muslim (and there were tons of Muslim merchants trading in Christian ports back then) you stood to not only lose your money but your freedom as well, getting sold into slavery.

Bottom line: you were constantly on the lookout while you were at sea and wary of any ship that approached.

Edit: added the part about contracts and treaties.

In the Roman Republic pirates were relatively common and would raid coastal towns in the Mediterranean and Asia ,as well as grain shipments headed to Rome from Egypt. The pirate problem reached a point that in the 60sBC a general (Pompey the great) was assigned to deal with the pirates that were raiding the Mediterranean, however, even after the appointment of Pompey and his claim that the pirate's fleet had been "defeated" ( more likely that he negotiated some form of deal or truce) in the 50s BC the Cilician pirates still remained a problem for Rome's sea trade. Julius Caesar in his younger life was also captured and ransomed by pirates.

This is going to primarily be about pirates that sailed in the 1690s-1720s.

For how likely, it all depends. Year, time of year, region of the ocean, and what kind of vessel your talking about. Let's stick to merchants. Merchants were probably the most likely to see them since merchants were the prime target of pirates.
In the western hemisphere along the coasts of the New World, trade winds often dictated where ships would go, and trade routes were well established by the Golden Age of Piracy. Most pirates were former sailors of some kind before becoming pirates (in fact the majority of pirates found their way into piracy by encountering them during a pirate boarding a merchant and deciding to become a pirate there). Some years, piracy was terrible, to the point that practically no ships were moving in and out of port when they normally would. It also doesn't help when pirates sit outside of ports or significant choke points on trade routes and wait for merchants (Charleston, the Virginia capes, and the mouth of the Delaware river all suffered this a few times). The Bahamas had a perfect position from which to prey on shipping since so many ships went through the Florida Straights and could be used as a point from which to hit both the east coast of North America and the Caribbean.
At peak years, such as 1716-1718, Marcus Rediker has researched how many pirates went to sea in the Altantic (which includes the Caribbean) and estimates in his work Villains of All Nations that around 2,000 pirates were at sea at any one point during that peak, which meant between two and three dozen pirate crews were out and looking for ships to take. Pirates were going after the merchants, since besides essentials like supplies (food, drink, ammunition, repair items), they also had cargo that could be sold illegally to colonial merchants. Besides the profitability, merchants would be easier to take on that Navy ships. While a number of pirate crews looked to get "ships of force," Navy ships were actually equipped and manned to fight - and pirates wanted to minimize risk to their operations and their lives (so the pirates often tried to avoid Navy ships). 4 easy to reference encounters between pirates and Navy men resulted in either death or defeat for the pirates. Blackbeard and Bartholomew Roberts were both killed in combat against Navy men, and Stede Bonnet and Samuel Bellamy both tried and gave up after casualties (in Stede Bonnet's case, severe casualties which included being wounded himself).

Does that answer your question? I guess the simplest way to answer it (or the TL;DR) is: In times when pirates were really active, merchants had a much higher chance of encountering pirates since pirates would seek them out as valuable and easier targets (and knew where the merchants would more than likely show up at sea since pirates were mostly former sailors).
Much of my information presented here (and a good book if you want to learn more about pirate strategy and tactics) is Benerson Little's Sea Rover's Practice.

If that is ok, I would like to request an answer to this question specifically in the golden age of piracy.

EDIT: has been replied here

Your question is very generalized, so please excuse my reply as being necessarily broad, but here goes:

Pirates generally used a variety of tactics to capture their prey. Some pirates pretended their ship had been disabled by a storm or other catastrophe. In general, it was considered good policy to stop and help the stranded vessel for two reasons: First, if everyone was dead already, more cargo and salvage for you and second, you might find yourself in a similar situation one day and you don't want to be passed by as well. Most of the time, the seas (regardless of time and location) were dangerous enough that disabled vessels were not completely unheard of, and most were legitimate shipwrecks. So, occasionally, you might get a faker who was luring you in with the old 'disabled ship' trick, resulting in a surprise attack from people you were trying to help. This method requires relatively simple weapons (everything from knives and belaying pins to guns and swords) and really can net a canny pirate some really nice loot and possibly a nice ship.

Another method was having a fast ship; maneuverability and speed are key to most piratical attacks as you can hit your enemy and move out of range of his reply, or close the distance and force a confrontation. Merchant ships are, by their very nature, relatively slow and cumbersome, leading pirates to target them as easy prey. Still, despite these facts, piracy was infrequent enough - or maybe profit was enough of a motivator - that merchants were willing to take the risk. Sometimes, however, merchant ships got lucky and came across a regular patrol of their own (preferably) navy or at least a navy ship more hostile to the pirate than the merchant's country. As sea lanes became more well-patrolled and military ships became better equipped to take on and defeat pirates, merchants generally felt safe enough to ply even 'dangerous' waters, hoping to score a huge profit.

A really god example of this is in the American experience with the Barbary Coast pirates. When the 'colonies' were under the protection of the British navy, piratical attacks in the Mediterranean were infrequent enough for viable markets for American products (such as lumber) to be established. After independence, however, Americans were foolishly expecting the British to continue to protect American ships from the Corsairs of Morocco, Libya, Tunisia, and Algiers (the "Barbary Coast"). What a surprise, then, when American ships began to be picked on by these pirates. The Corsairs found American ships easy pickings and so went looking for them; their cargo and even their crew were fantastic windfalls for the pirates and their masters. After independence, in order to secure the shipping of Americans from Corsair attacks, Barbary Coast pashas and Sultans received tribute from the United States. At its peak, nearly 1/6 of the Federal budget went to protecting shipping. Until 1801, anyway.

When Algiers demanded $1 Million for itself above and beyond the original tribute, the US declared war upon the Barbary coasts. Only after the Second Barbary War - when American patrols could forcibly protect American shipping - did piracy in the Mediterranean cease to be a real concern for the Americans.

Basically, a rule of thumb in any period of history is that if military patrols are sparse, pirates will gather and the result will mean a marked increase in the chance of encountering pirates for the merchant.

If you want to read a fascinating story of the most famous American to ever be captured by Barbary Coast pirates, read James Leander Cathcart's story published posthumously by his daughter The Captives: Eleven Years a Prisoner in Algiers (see: https://archive.org/details/captives00cathrich )

If book suggestions are alright, Empire of Blue Water: Captain Morgan's Great Pirate Army, the Epic Battle for the Americas, and the Catastrophe That Ended the Outlaws' Bloody Reign by Stephan Talty offers some insight to this subject in regards to the Caribbean during the 1660s-1690s.

How exactly did the pirates equip themselves at different periods of history? We all think of the "golden age" of piracy as fancifully imagined in film/literature/games, but what would a Roman or pre-Renaissance pirate vessel have used before reliable cannons?

Are there any interesting books or articles covering the piracy in the early medieval period?