Answer to Question #98144 in Statistics and Probability for C

Question

Please teach me how to draw Venn diagrams in probability,sometimes values are unknown and has x and -x,please do an example of Venn diagram and how I should start?im so confused,please help and explain in simple steps,Thanks

Answer 1

Let us look at an example o illustrate the process:

Given: $P(A∩B)=0.4, P(A∩B')=0.2$  and $P(A'∩B')=0.3$ .

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:

$P(B)=P(A∩B)+ P(A'\bigcap B)$

$=0.4+0.1$

$=0.5$

$P(A/B)=P(A∩B)/P(B)$

$=0.4/0.5$

$=0.8$ (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)

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