Answer to Question #302070 in Discrete Mathematics for BxJ

Question

Of 2000 persons under investigation (PUI) due

to Covid-19, 1050 PUI undergone rapid

testing, 500 PUI undergone swabtesting, and

200 PUI undergone both rapid and swab

testing. What is the probability that a

randomly selected PUI undergone random

testing or swab testing?

Answer 1

Let $R$ denote rapid testing, $S$ denote swab testing.

Given

$$P(R)=\dfrac{1050}{2000}=0.525, P(S)=\dfrac{500}{2000}=0.25,$$

$$P(R\cap S)=\dfrac{200}{2000}=0.1$$

The probability that a randomly selected PUI undergone random testing or swab testing is

$$P(R\cup S)=P(R)+P(S)-P(R\cap S)$$

$$=0.525+0.25-0.1=0.675$$