Question

The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?

Answer 1

4.6%.

Explanation:

The probability that a can of paint contains contamination(C) is 3.23%

P(C)=3.23%

The probability of a mixing(M) error is 2.4%.

P(M)=2.4%

The probability of both is 1.03%.

`P(C \cap M)=1.03\%`

We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e.
`P(C \cup M)`

In probability theory:

`P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%`

The probability that a randomly selected can has contamination or a mixing error is 4.6%.