Probability of my eye surgery success

jaan · #1 $Old$ May 1st, 2008, 11:30 AM

I'm having eye surgery next week to correct a long standing problem. Now, talking to my eye doctor he said the chance of success is about 90% per eye. I'm having both eyes done at the same time, and knowing how slippery probability can be something tells me that the success / failure rate might not be 90% / 10% for both eyes together.

Assuming the success rate is truly 90% each eye, what is the probability that both eyes will be fixed successfully?

What is the probability that at least one eye will be unsuccessful?

Thank you ahead of time...as you can imagine, this is something that's worrying me a great deal (c:

Moo · #2 $Old$ May 1st, 2008, 11:42 AM

Quote:

Originally Posted by jaan $View Post$

I'm having eye surgery next week to correct a long standing problem. Now, talking to my eye doctor he said the chance of success is about 90% per eye. I'm having both eyes done at the same time, and knowing how slippery probability can be something tells me that the success / failure rate might not be 90% / 10% for both eyes together.

Assuming the success rate is truly 90% each eye, what is the probability that both eyes will be fixed successfully?

What is the probability that at least one eye will be unsuccessful?

Thank you ahead of time...as you can imagine, this is something that's worrying me a great deal (c:

Hello,

Take the events L for left eye success, R, for the right eye.
These events are independent, which means that if one fails or successes, it won't influence the other eye's success/failure.

The probabilities $P(L)=P(R)=.9$

Hence, the probability for both eyes to success is known as $P(L \cap R)=P(L)P(R)=.81$

The probability that at least one eye is successful is : $1-P(\bar{L} \cap \bar{R})=1-\underbrace{P(\bar{L})}_{.10}\underbrace{P(\bar{R})}_{.10}=1-.01=.99$

CaptainBlack · #3 $Old$ May 1st, 2008, 11:44 AM

Quote:

Originally Posted by jaan $View Post$

I'm having eye surgery next week to correct a long standing problem. Now, talking to my eye doctor he said the chance of success is about 90% per eye. I'm having both eyes done at the same time, and knowing how slippery probability can be something tells me that the success / failure rate might not be 90% / 10% for both eyes together.

Assuming the success rate is truly 90% each eye, what is the probability that both eyes will be fixed successfully?

What is the probability that at least one eye will be unsuccessful?

Thank you ahead of time...as you can imagine, this is something that's worrying me a great deal (c:

Assuming that the probability of success is independant for each eye, the probability of both being successfull is 0.9*0.9=0.81 or 81%

The probability of both being unsuccessfull is 0.1*0.1=0.01 or 1%.

So the probability of only one being successfull is 1-0.82=0.18 or 18%.

RonL

jaan · #4 $Old$ May 2nd, 2008, 09:49 AM

Thank you for the reply...I'm feeling a little better about the surgery now, the odds aren't all that bad (c:

TKHunny · #5 $Old$ May 2nd, 2008, 10:15 AM

The only real problem with this anlysis is that it does not tell the whole story. Your surgery will go well or it will not. The problem with these percentages is that you cannot know ahead of time which group you are in. The percentages apply to POPULATIONS, and absolutely NOT to individuals. The important information is why do surgeries fail? If they fail because of incompetence, make sure you check out your Dr. very carefully. If they fail because of other patient factors, exactly what are those factors? Do you have them? Can you control them?

My point is that it is not really up to the percentages whether or not your surgery goes well. Please go to every effort to control all the factors you can control. It just isn't like rolling dice.

Social Note: When rain is forcast as a 50% chance, are we upset if it does or doesn't rain? How about 60%? 90%? What about 10%? Again, these are POPULATION statistics and their direct application to a single event is just wrong.