Error (probability bug) in childrens toys missions
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Join Date: Jun 2012
12-12-2012, 06:42 PM
Originally Posted by
Bottom line... is if it says 40% purple... that DOES NOT mean that 4 out of 10 will be purple. To be frank your understanding of probability is lacking.... don't feel bad most people don't understand much beyond the basic concepts.
A basic assumption in probability theory is that each event is independent of all other events. That is, previous draws have no influence on the next draw. So really because you pulled 1000 greens doesn't mean you are anymore likely to land a purple on your next try then; you had on the first of the 1000 greens you pulled. Even if the purple chance was 99% it would be unlikely you would pull 999 out of 1000 purples.
Yes, it does not mean you will get 40% purple. However, this probability means that chances are you will get an answer close to 40%, if you do multiple attempts. Assuming a binomial distribution (all trials independent, success/failure only), you will get a bell-shaped curve with the highest probability at 40% successes. The curve's spread will be less wide as number of trials increases. So, yes, the probability of getting exactly 40 may be pretty small. However, the chances of getting close to 40% successes is definitely quite high, compared to getting anything else.
Oh yeah, and 99% with 1000 attempts gives 990 successes as mean.
The issue with this thread is 20% DOES not ever = 20 in 100.... that is a possible outcome, however there is more math we could use that would show how small the chances of landing on 20 of 100 would be. lol
Yeah, you'll get a pretty small chance of landing on exactly 20 out of 100. However, what we're doing here is getting values close to 20, which is a perfectly legitimate way of testing the actual probability of success, due to the bell curve shape. Also, despite the probability of landing on 20 being small, the probability of landing on any other number is even smaller.
TL;DR: You've got a few problems with understanding probability yourself.