Let us look at an example o illustrate the process:
Given: "P(A\u2229B)=0.4, P(A\u2229B')=0.2"  and "P(A'\u2229B')=0.3" .
Find "P(B)"  and "P(A\/B)" .
The given data translates into the following Venn Diagram:
Now, there is one unknown region in the diagram. Let us denote this probability by "x" .
"\\implies P(A'\\bigcap B)=x"
The total of the probabilities in the sample space is always equal to 1.
"\\therefore0.3+0.2+0.4+x=1"
"\\implies x=1-0.9"
"=0.1"
"\\implies P(A'\\bigcap B)=0.1" . (Answer)
Now that all values in the Venn diagram are known, the required probabilities can be found easily:
"P(B)=P(A\u2229B)+ P(A'\\bigcap B)"
"=0.4+0.1"
"=0.5"
"P(A\/B)=P(A\u2229B)\/P(B)"
"=0.4\/0.5"
"=0.8" (Answer)
(Since "P(A\/B)" is the conditional probability of A occurring given that B has already occurred, our sample space gets restricted to the event B happening only)
.
Comments
Leave a comment