# Do odds increase over time based on brute force?

Attempting to understanding a statistical concept which I'm positive is basic stats, but that I currently don't understand. Say that there's a one in ten million likelihood of an outcome happening during an event, that happens a given count of times, and each time is roughly unrelated/correlated to another event. Do you the overall odds of the outcome happening change based on the count of events or not?

For example, say the odds are one in ten million that an outcome will happen and the event occurs 25 times. Is the outcome more likely, and if so, what is an explain of this, and how do the odds change from the one in ten million.

That depends on the process generating these outcome, but if you think of a "memoryless" process where each outcome is independent of the previous ones, such as flipping coins, then it doesn't matter how many heads you flipped in the past, the probability of flipping heads in the next flip is always 0.5.

• I think the OP is asking about what happens to the probability of observing at least one heads as the number of tosses goes to infinity. – Dimitriy V. Masterov Oct 22 '14 at 18:27

The probability of the outcome occurring at one specific opportunity never changes.

However, the probability that the outcome occurs within a set of opportunities does change based on the size of that set.

Coin flip example:

What's the probability this flip will be "heads"? 50%

What's the probability that I get at least one "heads", if I flip the coin ten times? 99.9%

So if, for example, your goal were to get "heads" at some point, continually flipping the coin will increase the probability that the event occurs at least once (but not that any individual flip will be the one that resulted in "heads").

• +1 Okay, sort of the issues I was thinking about. So, if you had an one in ten million likelihood of an outcome per "flip" what would the odds be if you "flipped" 25 times? – blunders Oct 22 '14 at 18:41
• @blunders: calculate the probability in reverse and subtract it from 1. Ex: (1 in 10 million) chance the event happens translates to (9999999/10000000) chance it does NOT happen. Thus, (9999999/10000000)^25 is the chance it does NOT happen (at all) in a set of 25 tries. Then subtract this from 1 to get the chance it DOES happen in a set of 25 tries – Joe Murray Oct 22 '14 at 18:50