Is it random?

[RealFunnyFungi]

Hey guys. As we all know that if we flip a coin, the possibility/probability of getting a tail or head is 50%.

 

Suppose a man is flipping the coin and record the results, say , 10 times.

 

The probability of getting all heads or tails is 0.5^10 = 9.765625x10^-4 which means that the probability is extremely small.

 

Now, if the man has a result of 10 heads. The experimental probability of getting heads = 10/10 = 1

 

In that case, is there still any probability existing while we are flipping coins???

[baxtrom]

Another one: if a guy throws a dart at a wall, the probability the dart will hit one predefined exact spot is P=0. Still, unless the guy is very poor at throwing darts and hits floor or foot or similar, he will hit an exact spot on the wall, so probability for apparent miracle (P=0) is P=1.

 

It's not a paradox, just the wrong way of using statistics. I'll leave it to the math gurus to come up stringent formulations involving sets, measures, distributions, generalized functions et c for proving it.

[ajb]

Now, if the man has a result of 10 heads. The experimental probability of getting heads = 10/10 = 1

 

If the coin is a fair coin, then as you state the probability of getting 10 heads in 10 flips is low, but not zero.

 

Still assuming the coin to be a fair coin, your man manages to get the outcome of 10 heads in 10 flips. This is one experimental outcome of a many possible outcomes. Probability still pays a role in predicting the outcomes and crucially the chances of each outcome being realised.

 

Now, if you are saying that your man managed to get 10 heads in 10 flips and that he was always going to get that outcome, that is the coin is "maximally unfair" probability plays a trivial role. The probability of getting 10 heads in 10 flips is 1 and all other conceivable outcomes have probability zero.

[CaptainPanic]

Hey guys. As we all know that if we flip a coin, the possibility/probability of getting a tail or head is 50%.

 

Suppose a man is flipping the coin and record the results, say , 10 times.

 

The probability of getting all heads or tails is 0.5^10 = 9.765625x10^-4 which means that the probability is extremely small.

 

Now, if the man has a result of 10 heads. The experimental probability of getting heads = 10/10 = 1

 

In that case, is there still any probability existing while we are flipping coins???

There is probability before you flip a coin, but not afterwards. Afterwards you have a measured result.

however, you can use the result of a previous experiment to predict something about another future experiment. (For example, if you get 10/10 heads, you might make a suggestion that the coin is not a 50/50 chance coin).

[RealFunnyFungi]

There is probability before you flip a coin, but not afterwards. Afterwards you have a measured result.

however, you can use the result of a previous experiment to predict something about another future experiment. (For example, if you get 10/10 heads, you might make a suggestion that the coin is not a 50/50 chance coin).

Does it imply that the randomness or i should say probability is eliminated after we finish flipping the coins?

[CaptainPanic]

Does it imply that the randomness or i should say probability is eliminated after we finish flipping the coins?

I think it's better to say that uncertainty is reduced (or completely eliminated) by measuring something.

 

And in the case of flipping a coin, a "measurement" is really simple: you just look whether it's heads of tails. No tools required, other than your own eyes.

Edited May 5, 2011 by CaptainPanic