Saving Private Ryan, which is probably the most renowned depiction of D-Day, seems to present it as a maelstrom where men are cut down seemingly arbitrarily. Is that what combat was like? Were a soldier's chances of survival equally arbitrary once they plunged into the water and began to make their way towards the pillboxes?
Additionally, is this the case throughout history? Superior numbers and weaponry aside, is it a game of a chance who lives and who dies in military conflict?
Decisions, skills, and leadership can only do so much for an infantry unit forced into combat. Other variables often decide how deadly a battle can be.
Omaha Beach had various units suffer between ~30% - ~100% casualty rates. A casualty is a person who is wounded or killed. Your chances of becoming a casualty on the first wave of Omaha beach were significantly high.
At Omaha Beach, the 116th RCT (Regimental Combat Team) from the 29th Infantry Division landed on Omaha beach. Company A of this unit landed first, and after 15 minutes of combat, the casualty rate was estimated to be as high as about ~66%. 66 out of 100 men were either dead or wounded after 15 minutes. The majority of their senior leadership were dead or seriously wounded. They were combat ineffective at that point.
A Ranger Company landed near Company A of the 116th, and it suffered a ~55% casualty rate by the time it reached the base of the cliff.
The other units that landed after Company A suffered casualty rates that reached up to ~50% (depending on which unit).
As far as your "chance" of death in combat, their are a lot of variables that increase or decrease your chances of survival in combat. The big problem with Omaha beach was how "open" it was, so the best thing you could have done to protect yourself in a combat situation is to get out of the open as quickly as possible.
Additional readings on Omaha Beach:
http://www.29infantrydivision.org/WWII-Battles/Omaha-Beach/index.html
http://www.militaryhistoryonline.com/wwii/dday/omaha.aspx
Additional information on combat:
This is long, wordy, but it explains a lot about combat and staying alive:
http://ttp2.dslyecxi.com/tactics.html
This is a video that talks about a lot of the same things using the ARMA 3 'simulation' from the same former soldier:
Cheers and enjoy!