How to differentiate between dependent and independent probabilities

Question

How does one differentiate between dependent and independent variables? Please provide examples

Answer 1

So, there's two different questions here (independent versus dependent variables, and independent versus dependent variables).

For probabilities:

1. A dependent probability is affected by the outcome of other events.
2. An independent probability is not affected by the outcome of other events.

An example of a dependent probability would be the probability of there being thunder tomorrow. The probability of it thundering tomorrow is higher if it also rains, so the probability of thunder is dependent on the probability of rain.

An independent probability would be a coin flip. The odds of "heads" on a coin toss is 50%, regardless of what the previous flip was.

For variables, an independent variable is what is controlled, and a dependent variable is your response.

Consider a problem involving the relationship between hours spent studying, and the resulting test score. Hours spent studying is what we can control, so it is our independent, or "x" variable, while the resulting test score is the effect, so it is our independent, or "y" variable.