City-Data Forum Calculating Risk (analysis, stock market, number, market)
 User Name Remember Me Password [Register]
Please register to participate in our discussions with 2 million other members - it's free and quick! Some forums can only be seen by registered members. After you create your account, you'll be able to customize options and access all our 15,000 new posts/day with fewer ads.

11-26-2012, 07:11 PM
 1,794 posts, read 3,630,982 times Reputation: 939

If someone has a 1% chance of an event occurring each year, what is the percent chance after a total of 10 years? Is it 10% - 1% + 1% + ...(10 times)?

11-26-2012, 09:21 PM
 5,810 posts, read 10,373,479 times Reputation: 5318
Quote:
 Originally Posted by djxpress If someone has a 1% chance of an event occurring each year, what is the percent chance after a total of 10 years? Is it 10% - 1% + 1% + ...(10 times)?
Yes, but there are a lot of caveats to it. For one the chances of something happening must be static which is a rare situation when you are doing risk analysis as conditions are changing over time. Second think about what it means if its already happened. In other words lets say you are calculating the chances of a 50% loss in the stock market and figure it has a 1% chance any year. What happens if its year 2 and the 50% drop happens. Is the risk of another 50% loss still there? Probably not. You can't necessarily account for that up front, but realize it does affect your risk probabilities as well.

But if you are doing something scientific like drawing a marble randomly out of a bag of 100 marbles and replacing the drawn marble after each draw and one of the marbles is red, then your chance of drawing a red marble is 10% over 10 draws. Notice there is a possibility you draw the red marble numerous times, but your chance of drawing it at least once is 10%.

11-26-2012, 09:38 PM
 1,794 posts, read 3,630,982 times Reputation: 939
I get your logic but then here is another scenario:

Lets say there is a 50% chance of an event occurring each year, like getting in a car crash. That would mean that over 2 years there would be a 100% chance of this event happening - 50% + 50% = 100%. This doesn't seem logically correct, as there is a 50% chance each year that you don't get in a car crash. So if you didn't get in one the first year, you'd still have a 50% chance of not getting in one the second year, there is a possibility of not getting in a crash over the two years, which means that the 100% likelihood is invalid.

Last edited by djxpress; 11-26-2012 at 09:53 PM..

11-26-2012, 09:43 PM
 20 posts, read 37,926 times Reputation: 15
10% doesn't seem right to me either. That would mean if performed 100 times at 1% there would be 100% chane of it happening. There has got to be a .9 in there somewhere.

11-26-2012, 10:05 PM
 5,810 posts, read 10,373,479 times Reputation: 5318
Quote:
 Originally Posted by djxpress I get your logic but then here is another scenario: Lets say there is a 50% chance of an event occurring each year, like getting in a car crash. That would mean that over 2 years there would be a 100% chance of this event happening - 50% + 50% = 100%. This doesn't seem logically correct, as there is a 50% chance each year that you don't get in a car crash. So if you didn't get in one the first year, you'd still have a 50% chance of not getting in one the second year, there is a possibility of not getting in a crash over the two years, which means that the 100% likelihood is invalid.
The math is wrong because you are doing something different here. If something is 50/50, there is the positive and negative of each event. So the chance of having 2 car crashes is 0.5*0.5 and the chance of 0 car crashes is 0.5*0.5. In other words have 25% chance of having 2 crashes, 25% chance of having no crashes and 50% chance of having exactly 1 crash.

As I mentioned in my other post, the chance of a 1% occurrence happening AT LEAST once is 10%. But there are a number of potential outcomes than 1 or none.

11-26-2012, 10:06 PM
 20 posts, read 37,926 times Reputation: 15
Quote:
 Originally Posted by djxpress I get your logic but then here is another scenario: Lets say there is a 50% chance of an event occurring each year, like getting in a car crash. That would mean that over 2 years there would be a 100% chance of this event happening - 50% + 50% = 100%. This doesn't seem logically correct, as there is a 50% chance each year that you don't get in a car crash. So if you didn't get in one the first year, you'd still have a 50% chance of not getting in one the second year, there is a possibility of not getting in a crash over the two years, which means that the 100% likelihood is invalid.

25% chance of going 2 years without a crash.

11-26-2012, 10:20 PM
 20 posts, read 37,926 times Reputation: 15
All right. I cheated Drop chance probability

11-26-2012, 10:29 PM
 1,794 posts, read 3,630,982 times Reputation: 939
that drop chance calculator seems to give more realistic numbers. It says that in 2 years with 50% chance each year the cumulative will be 75% which seems a lot more realistic than 100%.

When I took math, I could have sworn that we were taught that you take the odds (per event or per year) and add them up for the cumulative...guess that's incorrect

11-26-2012, 11:25 PM
 5,810 posts, read 10,373,479 times Reputation: 5318
Quote:
 Originally Posted by djxpress that drop chance calculator seems to give more realistic numbers. It says that in 2 years with 50% chance each year the cumulative will be 75% which seems a lot more realistic than 100%. When I took math, I could have sworn that we were taught that you take the odds (per event or per year) and add them up for the cumulative...guess that's incorrect
A lot of times what you are doing is calculating the chance of something not happening and then the inverse is the chance of it happening. This is the easiest way to think about the car crash scenario. Also remember the chance of something happening never should be 100% or 0% if there is probability involved.

11-27-2012, 06:57 PM
 Location: Upper East, NY 1,145 posts, read 2,832,357 times Reputation: 561
1- (0.99 to the 10th power). 9.6%
 Please register to post and access all features of our very popular forum. It is free and quick. Over \$68,000 in prizes has already been given out to active posters on our forum. Additional giveaways are planned. Detailed information about all U.S. cities, counties, and zip codes on our site: City-data.com.