PROBABILITY QUESTION

If I have a 41/2 % (4.5%) chance of an event happening every year from now on, at what point will it be even money that the event will occur?
Thanks.
rugcutter

I'm afraid that it will always be 4.5%

If however you're talking about it occurring or having had occurred, that's a different story.

I am sorry I didn"t make myself clear.

In how many years will it be even money that the event will occur?

You have to think about it in terms of NOT occurring. You have a 95.5% chance of the event NOT occurring in year 1. If you slip past year 1 then in year 2, you have another 95.5% chance of it NOT occurring.

0.955 * 0.955 = 0.912025

If you make it to the third year, the calculation is:

0.955 ^ 3 = 0.870983875

and so forth down the line until you goo below 0.50% in the 16th year

.955 ^ 16 = 0.47868954844692669363421067800579

But 15 Years is so close to 50% that I'll go with 15.

.955 ^ 15 = 0.50124560046798606663268133822596

I'm sure MathExtremist is about to yell at me.

Quote: rugcutter

I am sorry I didn"t make myself clear.

Don't feel bad something similar tripped up Marilyn of "Ask Marilyn" too.

Lemme see, I think you go with 95.5% chance that it will *not* happen. So on the second year [95.5% * 95.5%] there was 91.2025% chance it would not happen *either* year. Keep going with multiplying the result times 95.5% till you break 50%. Somebody will correct me if I am wrong. [edit: s2dbaker beat me to it]

Let him yell! It is exactly the information I was looking for, and I thank you!

Well, the only thing is, the math you're doing is saying that "it would have happened 50% of the time by now", but unfortunately in your case it still hasn't happened yet, and you're looking at another year of a 95.5% chance that it won't happen this year either. The math is just telling you how unlucky you have been in the past, it's not predicting the future for you, except to say that it's 95.5% that it won't happen again this year either. And, if you look at the history it's basically telling you that you've broke about even at the point where this event has a 50% chance of occurring by now. Of course, if it goes past the 50% mark, you're just really unlucky, or you're getting cheated, whichever the case may be.

Not yelling -- just pointing out that English tense structure and math often don't go well together. The phrases "something will happen" and "something will have happened" mean two different things. Your question is better asked "Starting from now, how many years would I have to look into the future in order to have a 50% chance that the event will have occurred during that timeframe?" Getting confused about where you are in time, and what future horizon you are considering, is one of the paths toward the gambler's fallacy or the belief in the maturity of chances. For example, using s2dbaker's 15 year period, the odds are roughly 50/50 that your event will occur at least once during that timeframe. But if it doesn't occur during the first 5 years, what do you know now?

A = 0 years
B = 5 years
C = 10 years
D = 15 years
E = 20 years

If you're at time A, the chance that the event will occur between A and D is 50%. If you're at B, and the event has not occurred, the chances that the event will occur between A and D is now lower than 50% (pop quiz: what is it?). If you're at B and the event *has* occurred, the chances are 100% that the event will occur between A and D because it already has. The problem is when you start looking at the span between B and D and suggest that it's still 50% even if it hasn't happened yet. It's not 50%. What *is* 50%, at that point, is the chance that the event will occur between B and E, or put another way, starting from B, that the event will have occurred by E.

If you're at B, and the event has not occurred, the chances that the event will occur between A and D is now lower than 50% (pop quiz: what is it?). If you're at B and the event *has* occurred, the chances are 100% that the event will occur between A and D because it already has.

Answering the (pop quiz). If you're at B, and the event has not occurred, the chances that the event will occur between A and D is now still 50%. The odds that it will occur between B and D is lower than 50%.

No. Tense matters. The chance *was* 50%, but it *is* no longer.