1. ## Penny probability

If you roll a penny 2 times and get heads both times, do you have a higher chance of getting tails on the third time you roll the penny.

2. ## Re: Penny probability

strictly speaking that depends on the penny but in general no, each roll is independent of all the rest and the probability of tails is 1/2

3. ## Re: Penny probability

But if you rolled a penny infinite times wont the amount of times tails was rolled and the amount of times heads was rolled eventually balance out in the case where you got lets say 8 heads in a row at the start?

4. ## Re: Penny probability

Originally Posted by kooltyme
If you roll a penny 2 times and get heads both times, do you have a higher chance of getting tails on the third time you roll the penny.
I have never heard of "rolling a coin". To flip a coin is the standard. The coin is sent flying in a rotating and then caught on the fly.
I was present at a session of a testing conference in which the speaker announced some of her talk had been rendered null by engineering faculty at he own university. It seems that they had proved that if a spinning coin were caught on the fly, there is no way that it being weighted could make any difference.
So if 'rolling a coin" is equivalent to "flipping" a coin it makes no difference. The probability is one-half.

5. ## Re: Penny probability

Originally Posted by kooltyme
But if you rolled a penny infinite times wont the amount of times tails was rolled and the amount of times heads was rolled eventually balance out in the case where you got lets say 8 heads in a row at the start?
you can say things about the next N flips with N>1

out of the next 2 flips it's more likely that you'll get 1 head and 1 tail than it is 2 heads or 2 tails

out of the next 100 flips it's more likely you'll see 50 heads and 50 tails than it is you'll see 1 head and 49 tails

but as far as the next flip goes the probability of a head or tail is 1/2 for both.

6. ## Re: Penny probability

Originally Posted by kooltyme
But if you rolled a penny infinite times wont the amount of times tails was rolled and the amount of times heads was rolled eventually balance out in the case where you got lets say 8 heads in a row at the start?
No! The "law of large numbers" says that on average the number of heads tends to equal the number of tails but that is only an average it says nothing about a particular sequence of flips (or rolls), even if that sequence is "infinite".

7. ## Re: Penny probability

For the OP: Of course, in this thread we are all assuming that the penny being "rolled" isn't a "trick" penny. Naturally, if you flip your penny lots of times and consistently get more heads than tails you might begin to suspect something strange is going on. Maybe it is a "trick" penny or maybe something about the environment is affecting the odds like you might find in a carnival booth. Now it becomes a statistics problem where you might try a hypothesis test $P(H>\frac 1 2)$ against the null hypothesis $P(H = \frac 1 2)$. Depending on the outcome of such a test you might be able to say with some certainty that the purportedly biased coin actually is biased. The degree of certainty with which you would make that statement depends on how many trials you use for your hypothesis test. And if the coin in the original problem is biased, of course that would change the answer to the question.