What is the probability that a randomly chosen chip has at least one of the defects?

Question

Aufgabe:

In the production of xy-chips the probability that a chip gets a wrong coding is 0.05. The probability that a chip has a defective surface has a defective surface is 0.08. The probability that a chip has both defects is 0.03.

Problem/Ansatz:

What is the probability that a randomly chosen chip has at least one of the defects ?

What is the probability that a randomly chosen chip has exactly one of the defects ?

Answer 1

Aloha :)

$$C=\text{wrong Coding}\quad\,\quad;\quad p(C)=0,05$$$$S=\text{defective Surface}\quad;\quad p(S)=0,08$$$$P(C\land S)=0,03$$

$$\text{1)}\quad P(C\lor S)=P(C)+P(S)-P(C\land S)=0,05+0,08-0,03=0,1$$$$\text{2)}\quad P(C\oplus S)=P(C\lor S)-P(C\land S)=0,1-0,03=0,07$$

Comments

Vielen Dank, ich habe durch mehrere Rechenwege verschiedene Lösungen erhalten. Jetzt weißt ich welche davon nicht richtig sind, dass hilft mir sehr viel weiter.