In a product there can be two types of defects: $A$ and $B$. The probability ($P$) of occurrence of defect $A$ is $0.1$ ($P(A) = 0.1)$. $P(B) = 0.2$. The two types of defects can occur independent of each other.
Let $X$ be a random variable that counts the number of types of defects in a product. Find the probability function.
In class we learned a general type of probability distribution (where you have to find the ad-hoc formula) and four special types of distributions (uniform, binomial, geometric and Poisson). I tend to think that I just need to find a custom formula for this one.
The random variable $X$ can be between $0,1,2$.
Let $C$ be the case when a product doesn't have any defects. $P(C) = 1 - P(A) - P(B) = 0.7$.
The case when there're 2 types of defects is $P(A \cap B) = 0.1 * 0.2 = 0.02$ (because it's given that $A$ and $B$ can occur independently).
The case when either $A$ or $B$ can occur is $P(A \cup B) = P(A) + P(B) = 0.1 + 0.2 = 0.3$
- $P(X = 0) = 0.7$
- $P(X = 1) = 0.30$
- $P(X = 2) = 0.02$
Not sure if I'm on the right track.