The key word in that sentence is "chance". Chances aren't guaranteed. This reminds me of the "100% chance of rain" weather forcast. 100% chance of rain does NOT mean it's going to rain. Just as a 50% chance of getting tails on a coin toss does not mean tails will occur half of the times you flip the coin.
Alas, no. Your logic is correct, but only under the assumption that each event has an equal likelihood. However, the odds in this case are stacked heavily against you becoming a millionaire. If your logic were correct, then there would be a 50% chance of any 'either/or' activity having occurred. However, no matter how ardently I wish it, my wife and I have yet to have a threesome with the local weather girl, nor have I been awarded the Nobel Prize. Given that there is by your reckoning a 50:50 chance of these events occurring on any one day, the odds are supremely in my favour that these events should have happened by now. :frowning:
Returning to the original topic, I personally can't see what the fuss is about. I don't think any statistician would argue that under perfect conditions that can be *exactly* replicated time after time, a result might be predicted with a high degree of accuracy. The point of coin tossing, like dice rolling or other forms of 'chance' is that in real life there are inevitably sufficient impurities in the procedure to guarantee a chance component.
I finally read the article, as I thought it was going to be along the lines of the discussion here, but I see it's not. What that professor found makes sense, and I'm suprised a machine was needed to see this. The laws of Physics should show that if performed the exact same under the same conditions, a coin flip is not random. However the act of flipping a coin by a person has so many variables it is effectively random and over enough attempts should be roughly 50%, minus the occasional edge landing.
Todd, I have to disagree with your logic completely. You're saying that because there are two outcomes, they chance of either is 50/50. That's ridiculous. You have to look at the causes of becoming a millionaire, do you have an invention on the verge of being sold, a relative about to die, a lottery ticket, or a stock that could take off? About the only other things left are a stranger giving it to you, a bank error, or stumbling across a bag of cash dropped from a plane or armored truck. You have to take the possibility of each of these things happenign to you and add them up, that's how you'll find the chance that you'll be a millionaire tomorrow.
By your logic, on one out of every two days I've lived, the following should have happened, death, been stricken with a horrible disease, gotten married, had sex, had children, had children die, become a millionaire, gone broke, killed someone, been involved in a terrorist incident, become a terrorist, and so on and so on.
The terrorist thing is a good example. On any given day you could die in a terrorist act. According to your logic that's a 50/50 chance every day. But the fact is over the last 100 years only 10's or 100's of thousands of people died in a terrorist attack (depending on your definition of course, I'm only counting bombings and shootings by the likes of the IRA, PLO, Al Quaeda, etc., not government acts). Based on that, and the fact that in the last 100 years there have been 7 or 8 billion, perhaps more, people that have lived, the chances of dieing in a terrorist attact are tiny, definitely not 50/50.
Sorry to rehash, but Keith made me think of something when he said:Two outcomes doesn't mean that each side is equal in probability. One side of the outcome could be 90% in favor of happening and the other side can be 10% in favor of happening.
So in the case of the millionaire thing, it's more like a ".001/99.999" chance that it will happen to you tomorrow. There's still two possible outcomes, but the numbers aren't equal for either side - as long as the two numbers equal 100, you're ok.
The study did show that even with the variables introduced by the person flipping the coin, there was a slight bias for the coin to land with the same side up as how it started. I believe it was stated that 51% of the time if it started with heads up, it landed heads up.
Gee, I thought this was finally going to be some evidence to support my claim that the tails side of a penny, is more aerodynamically grooved in it's design than the heads side, thus causing a wind viscosity effect, which rendors the tails side of the coin with a .0001726% advantage. This however all assumes that the cent piece in question is free of any pressing anomalies.