Recall that two events are independent when neither event influences the other. That is, knowing that one event has already occurred does not influence the probability that the other event will occur. How can we check whether two events are independent using probabilities? There are three simple ways to check for independence:
- Is P(A) × P(B) = P(A and B)?
- Is P(B|A) = P(B)?
- Is P(A|B) = P(A)?
If you answer yes to any one of these three questions then events A and B are independent. Also, if any one of these three is true the others are also true; so you just need to verify that one of them is true.
Example: Returning to the above Example 1 regarding being Female and getting an A, are events A and F independent?
With P(A|B) equal to 0.33 not being equal to P(A) which is 0.20 [this is applying independence rule number 3] then we can conclude that events Getting an A and Being Female are not independent (you can also conclude that these two events are dependent).