Here are some INDEPENDENT events:
- You flip a coin and get a head and you flip a second coin and get a tail.
The two coins don’t influence each other.
- The probability of rain today and the probability of my garbage being collected today;
The garbage will be collected, rain or shine.
Here are some NON-INDEPENDENT events:
- You draw one card from a deck and its black and you draw a second card and it’s black.
By removing one black card, you made the probability of drawing a second one slightly smaller. Technically this is called ‘sampling without replacement’.
The probability of a severe hailstorm today and the probability that the local airport will be closed to flights sometime today. Severe storms mean that airports sometimes need to close.
- The chance that you are hungry right now and the chance that you’re eating right now. Obviously one leads to the other eventually …
Showing that two events are truly independent events can be difficult, because you have to show that they don’t influence each other at all. However, lots of events are mostly independent, and therefore we can treat them as independent.