# Polyp probability

#### intric8

##### New Member
some help would be greatly appreciated, this should be easy for people here, but unfortunately i am bad with this stuff.

15 polyps are discovered in a patients large bowel. Each polyp has a 1 percent chance of becoming malignant in 5 years. Collectively, what is the chance that a malignancy will arise in 5 years? I'm assuming it is higher than 1 percent. Help?

#### GretaGarbo

##### Human
Is this homework?

Try the binomial distribution.

#### intric8

##### New Member
This is real life. I am not a student, just trying to assess what my uncle is faced with. Hope someone can help.

#### duskstar

##### New Member
If it is real life, then that is a question for a medical professional in my opinion. Statistics needs to have meaning put onto it, by someone who knows the medical area. I wouldn't want to answer that question for you. But, I wish you and your family well.

#### intric8

##### New Member
Perhaps i should rephrase my question.. it's really for my own edification about how these things work.

If there is a 5 percent chance of getting a particular result, and there are 15 of these events taking place simultaneously with the exact same probability, then collectively, what is the chance that one of these events will take place?

For example, if 15 cars of the same make and model, identical in terms of manufacturing, have a 5 percent chance of developing a fuel injection problem within 5 years.. well, what are the chances that one of these 15 cars will have a problem within 5 years? I'm quite sure you dont just add the probabilities up. Any help with this problem would be most welcome.

#### Dason

Well most likely you'll assume the outcomes are independent (if they aren't then we would need to know more information) but if that's an alright assumption you can just use the binomial distribution to answer your questions. For example with n = 15 and probability of 'success' of .05 the following table gives the probability of getting 0 successes, 1 success, 2 successes, ... and anything above 6 is pretty much negligible so I dropped that.

$$\begin{tabular}{cc} \hline \# Successes & Probability \\ \hline 0 & 0.4633 \\ 1 & 0.3658 \\ 2 & 0.1348 \\ 3 & 0.0307 \\ 4 & 0.0049 \\ 5 & 0.0006 \\ 6 & 0.0000 \\ 7 & 0.0000 \\ \hline \end{tabular}$$

#### lorb

##### New Member
Generally if you are given the probability of two independent events, the chance of both of the happening is the product of their individual probabilities. (If event A has probability 0.8 and event B has probability 0.5, the probability of "A AND B" is 0.8*0.5=0.4) By that pattern if the probability of no polyp turning malignant is 0.99 the probability of two of them not turning malignant is 0.99*0.99=0.9801. You don't need the binomial distribution to answer your question. The probability of at least one polyp becoming malignant is 1 - the probability that none of them turns bad. (but really ... this is so basic that google could have for sure answered you that)

edit for clarification: if this is indeed a real life case forget the math. polyps turning malignant is far from independent which is assumed in these calculations. I think duskstar got it just right:
If it is real life, then that is a question for a medical professional in my opinion. Statistics needs to have meaning put onto it, by someone who knows the medical area. I wouldn't want to answer that question for you. But, I wish you and your family well.

#### Dason

This is true and a point I was going to bring up. But in their last post they actually mention finding the probability of exactly one success. And for that you'll need to get into the binomial distribution.

#### intric8

##### New Member
I greatly appreciate your prompt responses and am thankful for this forum. I may not be communicating what i'm trying to understand properly here, and unfortunately, i'm barely a novice with this stuff. Tried googling the basic structure of this problem and i understand independent events somewhat, but can't find the basic answer to this problem. Came here as a last resort.

You would think that since these events are running concurrently, the chances would be increased? For example, Event A has a 5% chance of happening, that is simple to understand. Given 15 identical events (the same set???) with the same probability taking place at the same time, are the chances of just one event taking place increased?

I should clarify just one event, given the above scenario. Thanks for taking the time to help me with this

#### intric8

##### New Member
I'm sorry. Dason, so based on your numbers, the chance of one event occurring is 36.5%?

#### Dason

Yes. For 15 trials with a probability of success then the probability that you will observe exactly one success in the 15 trials is approximately .365. The main reason I put that table up though is that if you wanted to play around with the binomial distribution you would have a reference to see if you're computing things appropriately.

#### intric8

##### New Member
I completely understand. Thanks to you, i understand how a binomial calculator can help with this stuff. Much much thanks, and take care.

#### lorb

##### New Member
I greatly appreciate your prompt responses and am thankful for this forum. I may not be communicating what i'm trying to understand properly here, and unfortunately, i'm barely a novice with this stuff. Tried googling the basic structure of this problem and i understand independent events somewhat, but can't find the basic answer to this problem. Came here as a last resort
If you want to undersstand this stuff maybe watch some of those vids: http://www.khanacademy.org/#probability They are pretty good. Maybe you want to start with the one titled "Compound Probability of Independent Events". The guy really took some time and effort to make nice videos that explain this stuff. They are good.

You would think that since these events are running concurrently, the chances would be increased? For example, Event A has a 5% chance of happening, that is simple to understand. Given 15 identical events (the same set???) with the same probability taking place at the same time, are the chances of just one event taking place increased?
The fact that events are running concurrently is per se not a factor that increases or decreases their probability. It may give you a hint but if we take the polyps as an example: they are concurrent events but not independent because there exists some factor that influences them all in the same way. (Namely the disposition of the person towards polyposis syndromes which is genetic for most of them)