Binomial Probabilities

What does it mean to say that the trials of an experiment are independent?

Step-by-step explanation:

If I remember this correctly, if things/trials are independent then the result/outcome of one trial does not interfere or affect the outcome of other trials.

For example if you flip a coin 50 times. Each flip should be theoretically independent i. e. each head and tail should have 1/2 chance of showing up no matter what flip you make. It would not be independent if getting tails will give you heads next round for sure (it could happen by chance) but if one thing is causing another thing to happen it is not independent. Which means the probability of a coin coming up heads does not depend in any way on previous coin flips. The chance of getting tails on the next coin flip should be 1/2 as well.