Quintin Stafford

2022-06-25

The general addition rule for non-mutually exclusive is
P(A OR B) = P(A) + P(B) - P(A AND B);
Now I know how to calculate P(A) and P(B), but how do you calculate P(A AND B)?
Example: What is the probability of rolling a 5 or odd number? To find P(A AND B) in this case is very simple, we know without calculations that it is 1, right? But how to find P(A AND B) when there is a lot of counting to do... like lets say there are 9999 slots which are numbered, some are black some are white, some are even some are odd. Now to find the probability of getting a black and even when a die is rolled upon the slots, how to find P(A AND B)? or we just have to count it just like that?

Aiden Norman

Expert

If $A$ is "rolling a 5" and $B$ is "rolling an odd number", then is the event "rolling a 5 and rolling an odd number". The probability of that event is certainly not 1.
In general, there is no easy way to calculate $A\wedge B$, in some cases it's easy, in some cases it's hard. In some cases, it's easier to calculate $P\left(A\vee B\right)$. The only thing I can say is that you learn this thing by doing hundreds of exercises.

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Recalculate according to your conditions!