The sinking of the RMS Titanic resulted from a most unlikely culmination of events which cascaded one upon the next, ultimately ending with the loss of 1,514 passengers (710 were saved) and crew, not to mention a newly launched ocean liner.  The oversights and mistakes of Titanic's captain, Edward Smith, extended from well before the great ship was launched May 31, 1911 in Belfast, Northern Ireland, to the time the ship's band played Nearer My God to Thee, around 2:10 AM on April 15, 1912.  Notwithstanding the adage of  "women and children first," only 56 of the 109 children survived.

Perhaps what sets the Titanic's sinking apart from the thousands of others over the centuries is the astounding, indeed head-slapping mistakes that experts in their fields made, each one compounding the previous one in the critical path.  Had any one of these critical mistakes (or in some cases, simply random events) not taken place,  many hundreds of passengers and crew would have survived, and the Titanic as well.

Note this interesting warning sign just left of the flag at the stern:

Let's consider the a priori probability of the litany of errors, oversights, and shortcuts, all of which are my own personal estimates.   Use your own estimates just for curiosity.

Before he was given command of the Titanic on this, his final voyage before retirement, Captain Smith commanded the RMS Olympic, which on September 20, 1911, collided with the HMS Hawke, damaging one of Olympic's three driveshafts.  In the urgency of returning the Olympic to service, White Star Lines, its owner, scavenged one of the Titanic's driveshafts to replace Olympic's.  The Titanic's maiden voyage, scheduled for March 20, 1912, was thus delayed to April 10.  Nobody could possibly have known that this separate collision between two other ships would be Event One in the critical path which would culminate with the sinking of the Titanic and the tragic loss of so many innocent people who were simply traveling to America..

My estimate of the probability of Captain Edward Smith causing the minor but critical collision of the RMS Olympic, one of only two ships in White Star Lines, which delays construction and the launch date of the other White Star Lines ship, the Titanic, which Smith will subsequently command, and sink through compound foolhardiness
1 in 10,000.
 (One of Titanic's driveshafts was removed and installed in Olympic to get it promptly back into service)

Reduction of ship designer's original bulkhead height (steel wall, sectioning off parts of the ship below decks in case of serious water leak) ordered by White Star Lines President Bruce Ismay, in order to enhance ballroom design and customer comforts, ultimately at the supreme expense of the safety of ship, passengers, and crew
1 in 20

(After considerable reflection, I think these probability estimates of bulkhead height and lifeboat number should  be much smaller.  They compromise the safety of the ship, which should be a far greater concern to the ship's owner than beauty or comfort.  Nevertheless, I will leave them at 1 in 20, when 1 in 100 now seems more reasonable to me.)

The reduction of the number of lifeboats from 46 originally proposed by the Rule of 19th April, 1910, to 16 lifeboats as ordered by Bruce Ismay, Chairman and Managing Director of White Star Shipping, to save money and enhance passenger enjoyment had no bearing on the collision and sinking of Titanic, but it obviously had a profound effect on the number of fatalities.

Use of substandard #3 (instead of #4) cast iron rivets in curved forward section of Titanic, at a savings of mere pennies  (The #3 rivets were 9% slag instead of the standard 2 - 3% slag in #4 rivets.  This excess slag weakened the rivets, allowing the heads to pop off, and the plates to open up.)
1 in 10

According to documentation found in Harland & Wolf archives, plus some deep sea discoveries in both Titanic and its sister ship Britannic, it appears that J. Bruce Ismay ordered the builders of Titanic to use a thinner steel plate than originally specified.  There was possibly likewise a conspiracy to cover up the fact that the Titanic broke apart at only 11 degrees rather than the 45 degree angle shown in the movie.  This hastened the sinking by approximately two hours, a critical period of time that would have enabled the Carpathia to rescue hundreds of doomed passengers still on board.

Spontaneous combustion of coal in bunker six, from dust buildup, began during speed trials in Belfast ten days prior to the departure from Southampton.
1 in 500

The coal fire in Bunker #5 was not put out before Titanic left Belfast, seriously weakening the plates on the starboard side where the iceberg hit.
1 in 1000

A few days before Titanic set sail, Second Officer David  Blair was replaced by Charles Lightoller, and in Blair's haste to leave the Titanic, he forgot to hand the key to the binoculars locker to Lightoller for lookouts to use in the crow's nest.
1 in 10

Final photograph of the Titanic afloat, departing Southampton

Failure of Captain Smith to reduce speed from 21.5 knots (almost full speed) despite repeated warnings of icebergs (Smith was clearly eager to please his boss, Bruce Ismay, who wanted to set a record time for crossing the Atlantic)
1 in 10

Failure of Captain Smith to order crew to use tools and break into locker containing binoculars requested by ship's lookouts, to enhance safer navigation of the ship at night
1 in 50

Insufficient moonlight to disclose iceberg dead ahead, struck at 11:40 PM, April 14
1 in 10

Calm seas reduced wave action around the base of the iceberg, making it much more difficult to see until it was too late
1 in 5

Titanic radioman Jack Phillips failed to forward last and most critical iceberg warning to ship's bridge, as Californian had stopped dead in the water to avoid colliding with icebergs
1 in 50

Titanic radioman ordered Californian's communications room to "Shut up, shut up" as they attempted to warn of dangerous icebergs nearby, just ten minutes before Titanic hit the iceberg
1 in 20

The Californian's radio operator, Cyril Evans, shut his radio off at 11:30 PM after being told to "Shut up!"  Therefore he could not receive the subsequent SOS calls nearby.
(Captain Stanley Lord, commanding the SS Californian, ordered the ship to a full stop for the night to avoid collision with an iceberg.)
1 in 20

Spotting of iceberg by lookouts in the crow's nest was too late to avoid a collision, but early enough (37 seconds) to commence evasive maneuver which compounded damage beyond survivability - a 230 foot long tear in the Titanic's hull, flooding six separate compartments (Four flooded would not have sunk her.)   Had the lookouts been posted on the bow, forty feet lower, they may have seen the outline of the iceberg against the faint horizon sooner.   The ship's searchlight should have been lit to illuminate the path ahead, even though it was not standard procedure.  It was, after all, a moonless night with no waves washing against ice floes.
1 in 10

Watch officer throwing all engines in reverse while ordering the helm hard a-port, robbing the rudder of the authority it had while running.  (If instead he had reversed only the port engine, leaving the center and starboard engines in forward, or if he had reversed all engines while maintaining the original track, the Titanic might not have sustained fatal damage.  A direct hit surely would not have flooded all six compartments.)
1 in 20

Inexcusable failure of Captain Edwards or any officers to oversee filling all 20 lifeboats, 4 of which were collapsible, to rated capacity, much less to some arbitrary but reasonable number over theoretical capacity (say ten more people) in view of  the exceptionally calm seas
1 in 50

Failure of Captain Lord, of the SS Californian, twenty miles north, and in sight, to react immediately to distress flares reported to him by his crew  (He didn't even bother to summon his radioman to call the Titanic,  and inquire if there was an emergency.)
1 in 50

The compound probability of all successive events multiplied together is one chance in 2.5 x 10 to the 25th power, or about one chance in 25 trillion trillion.

I did not set out with a goal of some particular probability of the Titanic sinking.  I simply made my own reasonable estimate of each successive dependent factor.   Make different estimates of your own if you wish. Using your own estimates will give you a better idea of how unlikely the entire series of events was.

Each of the above factors is arguably on the critical path to the sinking and incredible loss of life. The Titanic might well have survived the collision if not missed the iceberg entirely, or alternatively, all 1,514 passengers lost might have been saved through the elimination of just one of the foregoing events, each of which contributed to the catastrophe.  It is noteworthy that there was, on average, 20 empty seats in each of the 20 lifeboats launched.  Moreover, an average of 12 crewmen occupied each lifeboat, when only 2 were needed to operate it.   Therefore the crewmen put their own lives and safety ahead of their passengers, for whom they were responsible.

[Note on the nature of estimating probabilities:  I have had many discussions on the topic of estimating probabilities on the subject of the marvelous, profoundly improbable nature of life and the universe around us, and the obvious, pervasive hand of our Creator.  Almost unfailingly, atheists make the absurd contention that if something happened, then the probability that it would happen was 1.  (Because it happened.)  The chance of you drawing the three of clubs randomly from a shuffled deck of cards is 1 in 52 before the event. Whether or not you actually did draw the three of clubs, the chances of drawing it were still 1 in 52.  Estimating probability is how we measure uncertainty, or likelihood, for an event or an event series.]


Now, suppose there had been one thoughtful officer on board, intent on saving as many passengers and crew as possible, as is every crewman's greatest responsibility.

If he had ordered:

1.  The crew to fill every lifeboat to capacity, confiscating all life jackets from women and children before they debarked.  In addition to the rated capacity, ten additional women and children were then loaded into each successive lifeboat launched.   Then, after all the children and women were safely away,

2.  Men to be loaded in lifeboats, likewise with ten additional passengers in each lifeboat over its rated capacity.  There was more than ample freeboard for such an overload, and the sea was calm.  These two steps alone would have saved an additional 668 people.

Survivors being picked up by the Carpathia.  Note the enormous freeboard of the collapsible lifeboat, and the calm sea.
The life jackets were unnecessary and more passengers could have been saved even in this lifeboat.

3.  Every able-bodied man on board to bring up on deck all wooden deck chairs, tables, and any furniture suitable for constructing as many wooden rafts as possible, and the deck kept clear of all passengers except those immediately boarding a lifeboat or constructing rafts.  There was more than enough wood on Titanic to build sufficient rafts to save hundreds.  Here is a tiny sample, showing wooden tables and chairs, in a small section of the Cafe Parisian.

Wooden chairs and tables in A La Carte Restaurant on B Deck:

4.  Every crewman to bring up on deck all hammers, saws, axes, wires, ropes, cables, straps, screws and nails suitable to fashion rafts with life jackets securely tied underneath them for buoyancy.  Fabricated wooden rafts would be stiffened with longer pieces of wood or lightweight metal rods and a minimum of two paddles fabricated per raft of ten by ten feet.  Simple boards would also work for paddles.  All men aboard rafts to remain seated at all times, for stability.

5.  Two officers and eight able-bodied men to take the first lifeboat and carry hand tools to the iceberg  and chip steps out and insert poles with hand ropes so that passengers and crew could climb off rafts, especially if there was an insufficient number of rafts constructed.  (Approximately 90 rafts holding ten men each would be needed in the event nobody could debark to the iceberg.  Even if that number rafts could not have been constructed, surely many could, and the loss of life would have been further reduced.)

Then that one wise senior officer would have saved a majority of the 1,514 who perished.   Casualties included super wealthy passengers John Jacob Astor IV and Benjamin Guggenheim.

This is the photograph of The Iceberg, smeared with Titanic's red and black paint.

Rescued passengers aboard the Carpathia

One of several letters written by survivors stating Captain Smith had been drinking on that fateful night.

Captain Smith's misadventures began even before his collision with the Hawke.

Approaching New York on her final White Star sailing, on January 27, 1889, Republic I runs aground off Sandy Hook and is refloated five hours  later. After she docks a 9 foot length of 38 inch  boiler flue explodes, scalding ten crewmembers, three of them fatally.  Republic's captain, Edward J. Smith, reports that damage to the ship is slight. Later in 1889, Republic will be sold to Holland America and  renamed Maasdam; still later, she'll be sold several more times and have several other names before being broken up in Genoa in 1910. (Sources:  The New-York Times, 28 January 1889; Eaton & Haas' Falling Star; Bonsor's North Atlantic Seaway.)

Arriving at New York with 881 passengers on board on November 4, 1909, Adriatic II goes aground at 3:20 a.m. on a sand bank at the entrance to  the Ambrose Channel. She is freed, undamaged, at 8:10 a.m. due to the  combined effect of a rising tide and the discharge of water ballast.

Adriatic's commander is Capt. Edward J. Smith. (Sources: New York  Herald, 5 November 1909; The Evening Post (New York), 4 November 1909.)