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Technically 1 out of 1 people who undergo that procedure die, eventually. Same is true for people who elect not to have the procedure done, eventually.

Doctor stabs you. "Oh no! Questioning the surgery claims another..."

Is the surgery incredibly risky overall but the surgeon only takes patients with the highest chances of survival?

I mean even then the stats can change with so many variables. It's kind of like how you have a 50% chance of surviving by splitting up with Sam. You both knew it had to be done- the forest was thick and you knew it could only stalk one of you. You wish you had more time with him, but someone had to survive to tell the tale.

As you get some distance and pray to God that you are alone, you crouch low and look for any sign of a trail or a building to get to. The fog is beginning to thicken as you decide to move downhill. Water flows downward, so this is the best chance you have to find a river.

You keep running as quietly as you can as the last glow of sunlight dissipates from above the trees. You begin to panic as you realize there's no hope for navigation in pure darkness. But then hope. The bubbling of water on rocks tells you that the river is just below. You cautiously move through the brush, heart pumping- were you being followed? It could have been waiting for the perfect moment- who knows how quietly it can move.

You get down to the river when you see a light on the other side. You focus on the shining and see it's a flashlight. Sam had taken the flashlight with him, is it possible your paths reconnected? You wade across the shallow current- the water is cold but maybe this means you two lost whatever it was miles ago. Your shoes press down on the pebble shores as you scrape your way up the bank. "SAM" you whisper "SAM HEY". No response. You slow down as you approach the flashlight laying on the ground. It was Sam's, but Sam was nowhere to be seen. You reach down as you feel rain drops slowly fall on you. As you grab the light you notice something- the raindrop on your hand is dark.

As you realize what you are seeing, you begin to shake, mouth agape. You feel another drop on your shoulder. You knew you shouldn't. You knew you should have accepted it and just moved on. You shouldn't have looked up.

There he was. The top half of Sam was dangling from the branches, his pale face looking down at you with blood streaking across his face and dripping off his nose. How could this happen? What could do this to Sam, especially since you knew he was the fastest man in your platoon. He was able to get to you with the ammunition you needed when you're whole unit was under fire in Kuwait. He saved your life, but you couldn't do the same for him.

The shock is broken when you hear heavy boots stepping in front of you. It was over. There was nothing you could do. Nothing you ever could do. It- he- whatever you would call the figure in front of you just stated back into your soul. You felt the rattling of your lungs as you took the last few breaths you ever would. The blood soaked hands that reached out through the darkness led up to the man of your nightmares. Bits of Sam falling out of his mouth, he is fully revealed. It was him. It was always him. It was always

But yea in order to answer this we should define our parameters a bit more.

Depending on what you're treating, 50% sounds pretty good.

I remember when I went for my last surgery and I was signing all the consent forms, my doctor was emphasising the 17% chance of this known lifelong complication, and the increased 4% chance of general anaesthesia fatality (compared to 1 in 10,000 for general public).

My mum was freaking out because when she had the same surgery she'd been seen much earlier in the disease process, she wasn't expecting such a "high" risk of complications in my care.

But all I was hearing is that there's an over 80% chance it will be a success. Considering how limited and painful my life was by the thing we were treating, it was all no brainier, I liked those odds. Plus my condition is diagnosed 1 in 100,000 people, so how much data could my surgeon really have on the rate of risk, the sample size would be laughable.

Still the best decision of my life, my surgeon rolled his skilled dice, I had zero complications (other than slow wound healing but we expected and prepared for that). I threw my crutches in the trash 2 years later, and ran for the first time in my life at 27 years old after being told at 6 years old that I'd be a full time wheelchair user by 30.

10 points to Gryffindor

Depends on the sample size.

If it's just this guy doing it, then yeah.

If it's this guy who has done the procedure 20 times with 20 successes, and another doctor who sucks, who performed the procedure 20 times with 20 fatalities, that's different.

It's likely that the sample size is much larger than one or two doctors.

The normal person thinks that because the last 20 people survived, the next patient is very likely to die.

The mathematician considers that the probability of success for each surgery is independent, so in the mathematician’s eyes the next patient has a 50% chance of survival.

The scientist thinks that the statistic is probably gathered across a large number of different hospitals. They see that this particular surgeon has an unusually high success rate, so they conclude that their own surgery has a >50% chance of success.

Mathematician sees each individual outcome as independent 50% chance.

Scientist realises that the distribution of failures and successes puts him in a favorable position. e.g. for the 20 in a row to be a success in a 50% fail rate that means the previous 20 were all failures or some similar circumstances where the success rate rose over time or similar polarization of outcomes in the sample data which places them above average odds.

You're assuming those 20 were the only ones. Zoom out.

The left 50% or the right 50%

no.

No, never.

Until vastly larger numbers of people get trained in Advanced Mathematics and Degree Level Scientific disciplines, the human norm will never be anywhere near Mathematicians and Scientists.

It's quite literally abnormal to be a Scientist or Mathematician.

Then again, so is being Homeless or an Olympic-level Athlete.