Let us assume that even F represents fidelity and event S represents selectivity.
We have been given the probabilities:
P(S) = 0.72, P(F) = 0.59 and [tex]P(S\cap F)=0.33[/tex]
We need to find the conditional probability that a system with high fidelity will also have high selectivity. We know the conditional probability formula:
[tex]P(\frac{S}{F})=\frac{P(S\cup F)}{P(F)}[/tex]
Upon substituting the given values, we get:
[tex]P(\frac{S}{F})=\frac{0.33}{0.59}[/tex]
[tex]P(\frac{S}{F})=\frac{33}{59}=0.56[/tex]
