Understanding Probability and Fairness in Coin Tosses

[gilishaky]

Hi, i was wondering if some one could explain to me some things about probability.

How is probability determined is it based on a average or a small set of experimental data? If you were to flip a coin Randomly 50 times and you get heads 40 times and tails 10 times could you then say you have a 80% probability to get heads then tails?

I know that having a 50% probability for example in a coin toss doesn't mean you'll get head or tails 50% of the time, you just have a chance to but then how do you infer how many times you will get head or tails.

Also if you flip a coin and have 50% probability to land on heads and you don't land on heads does that change the probability? or is it still 50%.

 

[Stephen Tashi]

How is probability determined

Probability can't be determined by any series of measurements. Probability theory says that if we conduct independent experiments where the probability of an event is some unknown but constant value then the fraction of times this event occurs in the experiments will probably be close to the probability of the event. In physics, people often refer to "physical probability" and assume that enough repeated experiments are guaranteed to approximate the probability of an event to an arbitrary precision.

Using data from experiments we "estimate" probability. We don't "determine" it.

 

[bsheikho]

Assume that everything has an equal chance of happening. and based on constraints, adjust the chances of different events occurring accordingly.

 

[jbriggs444]

Assume that everything has an equal chance of happening. and based on constraints, adjust the chances of different events occurring accordingly.

Or look at https://en.wikipedia.org/wiki/Bayesian_probability

 

[CWatters]

If your coin is fair and can't land on edge then by definition the probability of getting a head or tail is 50%.

If you make a few coin tosses and don't get an equal number it didn't automatically mean the coin isn't fair. The question how many times must you toss the coin to determine if it is fair is quite complicated. See...

https://en.m.wikipedia.org/wiki/Checking_whether_a_coin_is_fair

The field of statistics has quite a lot to say about confidence levels.