Question

The probability that a data communications system will have high selectivity is 0.72, and the probability that it will have high fidelity is 0.59, and the probability that it will have both is 0.33. find the probability that a system with high fidelity will also have high selectivity

Answer 1

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 $P(S\cap F)=0.33$

We need to find the conditional probability that a system with high fidelity will also have high selectivity. We know the conditional probability formula:

$P(\frac{S}{F})=\frac{P(S\cup F)}{P(F)}$

Upon substituting the given values, we get:

$P(\frac{S}{F})=\frac{0.33}{0.59}$

$P(\frac{S}{F})=\frac{33}{59}=0.56$