# What is probability ?

1. Jul 10, 2013

### malignant

I mean I know what probability is, but let's say you flip a coin 5 times and it's heads every time...then switch coins? that can't have any affect on it but what if you waited an hour after getting 5 consecutive heads and come back with those 5 heads in mind, you would probably pick tails. but if you had forgotten about it instead of remembering it, then you would say it's 50/50 again. so which one is "right"? is it 50/50 again or is it in favor of tails? or is it just an illusion?

2. Jul 10, 2013

### HayleySarg

I'm not entirely sure what you're asking.

Obviously variations in a coin may slightly alter the outcome(within the means of a rare-event rule case >5%) but the probability is still binary. It's either heads, or it's tails.

3. Jul 10, 2013

### malignant

I guess I'm asking if it ever "resets"? Like if you get 5 heads in a row, it's most likely going to be tails next but if you forget about the 5 heads then...yeah

4. Jul 10, 2013

### MarneMath

If we're assuming the coin is fair then there should be no difference between the two different but fair coins (assume each coin has the same probability.) Since each flip of a coin is independent, then it doesn't matter if you use a new coin each time if they have the same probability.

5. Jul 10, 2013

### krash661

it doesn't matter what you remembered,
it's still 50/50 because there's only two possible choices,

getting heads 5 times in a row,
is still only a 50/50 choice.
it just means out of the 50/50 heads came up.

6. Jul 10, 2013

### HayleySarg

Last edited by a moderator: May 6, 2017
7. Jul 10, 2013

### bp_psy

You are talking about two different situations . The probability of getting six heads in a row is not the same thing as the probability of getting a sixth head given that you already had a five head sequence. In the second case the probability of having the first five head sequence is 1 (you already have it) so the probability of getting the six heads is 1*1/2 =1/2.
http://en.wikipedia.org/wiki/Conditional_probability

8. Jul 10, 2013

### malignant

Oh I don't think I worded it right.

It's not exactly a mathematical question.

Say there's two sessions that you're going to flip coins, the second session is some unimportant time after the first. The main idea is that they're separate.

The first session you get 5 consecutive heads. If you had to bet money on the next flip, you'd pick tails because the probability of getting a 6th heads is 1/64. But if you decided not to flip the 6th coin until later on during the second session, keeping the 5 consecutive heads in mind, would you still bet money on tails?

During the second session, in your mind, you've still gotten 5 consecutive heads earlier during the first session so would you bet on tails or would you disregard it and pick one at random? If I was going to pick one at random anyways, then I would just pick tails because I have a slight reason to (the 5 consecutive heads earlier) even though it's always 50/50.

But in reality, what makes them separate and it not still being a 1/64 chance of getting a heads during the second session like it was after you got 5 heads in the first session? Basically what distinguishes 2 sets of probabilities at different times? Pure math doesn't really deal with time so that's why I said it's not really a mathematical question.

9. Jul 10, 2013

### malignant

that seems more related to what i was talking about. ill read up on it

10. Jul 10, 2013

### Office_Shredder

Staff Emeritus
This is wrong, and you actually know it even if you don't realize it. Suppose I just start flipping a coin a bunch of times. After 4 or 5 minutes I happen to flip five heads in a row. I turn to you and say "I bet you my 1 dollar against your 60 dollars that it comes up heads on the next flip"

If you think the odds of the next flip coming up heads is 1/64, then you should think my bet is a fair bet (even if you don't take it because most people don't like betting money on even odds). But most likely you're thinking that the bet sounds outrageous, because there's a 50/50 chance that the next flip is a heads vs a tails

11. Jul 10, 2013

### bp_psy

12. Jul 10, 2013

### MathJakob

You're misunderstanding. It doesn't matter if the coin lands on heads 100 times in a row, the next flip is still 50/50 to land on heads again no matter if you flip immediately or leave it for a day or even use a different coin.

Before I start flipping the coin if you asked me what is the propability to get heads 12 times in a row for example, then it would be 1/2048. But each individual flip has equal chance.

13. Jul 10, 2013

### malignant

i see now. only thing that's weird to me is how the outcomes always tend to even out right? like 1000 flips tends toward 500/500 so that's why i was thinking if it was say 999 heads then the final flip would more likely be tails. misleading on my intuition

14. Jul 10, 2013

### HayleySarg

15. Jul 10, 2013

### MathJakob

Psychologically you'd probably pick tails just because you'd say to yourself surely it can't be heads again... but it really makes no odds.

It's the same reason why people who play the lottery never pick 1 2 3 4 5 6 7 just because psychologically it is less likely the occur than 7 random numbers, even though it has exactly the same probability to occur than any other set of 7 numbers.

16. Jul 10, 2013

### zoobyshoe

Derren Brown did a coin flip thing. He bets the viewer he can get ten heads in a row. Then they show a continuous shot of him flipping a coin, and he gets ten heads in a row.

The 'trick' we find out, is that the clip shown was the final minute out of something like ten grueling hours of coin flipping. After all those hours, he finally, accidentally, got ten heads in a row.

I don't know what that says about probability.

17. Jul 10, 2013

### xxChrisxx

So you are saying that your brain is subject to gamblers fallacy. The correct answer is you'd just pick one at random.

The more smart *** answer is to bet on heads, with a disproportionate amount of heads over a sample size, the more likely the coin is biased.

18. Jul 10, 2013

### 256bits

Well not exactly, that is not quite correct. For a a coin toss, as the number of tosses increases the percentage of heads or tails tends towards the mean of 50%.. The actual number of heads and tails will diverge from the mean of equal number of heads and tails.

19. Jul 10, 2013

### MathJakob

If you made a computer that picked a number from 1 - 10 after an hour of picking millions of numbers you'll see that 1,2,3,4,5,6,7,8,9 and 10 are all picked the same amount of times, well almost the same and the longer the program runs the closer the averages get to being equal.

Isn't this just the law of averages?

20. Jul 11, 2013

### malignant

no, that's not what i was referring to but my post had errors. i meant according to the law of large numbers or law of averages or whatever you want to call it. so it wasn't really a gamblers fallacy. i see now that the next flip is still 50/50 but i meant more as a whole.