Need Help Re: Probability vs. Degree of Certainty

I am trying to determine a coin toss.

If I toss a fair coin 9 times and I get 7 "Heads"... what is the best way to predict what will appear on the 10th toss?

I have tried( Binomial Probability) and also used (Odds in favor and odds against) to try and calculate the answer... and the best success I have had in predicting the 10th toss is about 60% (which is not much above 50/50 or P = .5)

My Question: Is there a better way to predict the 10th coin toss with a higher degree of certainty? Should I be looking at Intervals or Confidence Intervals? What am I missing?

Thanks

Have you considered the negative binomial?. It is a little different than the 'regular' binomial.

\(\displaystyle \binom{n-1}{k-1}p^{k}(1-p)^{n-k}\)

It is used when we are interested in the number of the trial on which the kth success occurs.

Say, we want to know the probability of the 8th head occuring on the 10th try.

\(\displaystyle \binom{9}{7}(\frac{1}{2})^{8}(\frac{1}{2})^{2}=\frac{9}{256}\approx .035\)

Does this help?.

Thanks Galactus. Yes.. I have tried the negative Binomial

I was using a Cumulative Binomial Calculator, and still was only able to accurately predict the tenth toss correctly about 50% of the time.

(this is not part of any mathematical formula.. I just did an informal test on my own. I did a series of 12 experiments... each time...trying to predict the 10th coin toss. And I could only guess the correct answer about 50% of the time.)

Sometimes I got 5 heads out of 9 tosses... sometimes I got 8 heads of of 9 tosses... sometimes I got 2 heads out of 9 tosses... I then plugged these number into the Cumujlative Binomial Calculator. I could only get a success rate of 50%.

I understand that on a 2 sided fair coin.. P is always going to be .5... but I thought if you added the Cumulative P.. you would get a more accurate prediction...?

So I am perplexed. There must be a way to more accurately predit the 10th coin toss?

Thanks again.

The prediction for the 10th toss is the same as any other toss. It is .50

We have a .50 probability of tails and a .50 probability of heads on each trial.