Question

If $A$ & $B$ are two events such that $P\left(A\right)=0.6$ & $P\left(B\right)=0.8$, then the greatest value that $P\left(A/B\right)$ can have is

• A. $0.70$
• B. $0.75$
• C. $0.80$
• D. $1$

Answer 1

The correct option is B $0.75$

First of all, $P\left(A/B\right)=\frac{P(A\bigcap B)}{P\left(B\right)}$

Now, it is given that $P\left(B\right)=0.8$

So for maximizing $P\left(A/B\right)$ , we have to maximize $P(A\bigcap B)$ .

Notice that, if we draw the Venn Diagram of the above probability chart, if event B completely overlaps with event A, we get the maximum intersection area between the two. In that case, the entire probability region of A is the overlapping part. Thus for maximum intersection,

$P(A\bigcap B{)}_{maximum}=P(A)=0.6$

$P(A/B{)}_{maximum}=\frac{P\left(A\right)}{P\left(B\right)}=\frac{0.6}{0.8}=0.75$