Help pls trying to understand

[pineappleshark]

If A and B are events such that P(A)=0.2 and P(AUB)=0.9, find P(B) when:
a) A and B are mutually exclusive
b) A and B are independent

 

[Dr.Peterson]

Write the formula for P(A∪B). It includes P(A∩B).

What can you say about P(A∩B) when A and B are mutually exclusive?

How about when A and B are independent?

Now use the resulting equations to solve for P(B).

 

[Steven G]

Probability (like most math) is like a game which you can't play until you know the rules. You must be able to answer Dr Peterson's questions before you have a chance on answering your questions

 

[pka]

If A and B are events such that P(A)=0.2 and P(AUB)=0.9, find P(B) when:
a) A and B are mutually exclusive
b) A and B are independent

We know that in general \(\displaystyle \mathscr{P}(A\cup B)=\mathscr{P}(A+\mathscr{P}( B)-\mathscr{P}(A\cap B)\)
a) If \(\displaystyle A~\&~B\) are mutually exclusive then \(\displaystyle \mathscr{P}(A\cap B)=0\)

b) If \(\displaystyle A~\&~B\) are mutually independent then \(\displaystyle \mathscr{P}(A\cap B)=\mathscr{P}(A)\mathscr{P}(B)\)