How to find the probability of declaring faulty My question: Consider a company that assembles computers. The probability of a faulty assembly of any computer is $x$. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of $y$. what is the probability of a computer being declared faulty? I am a $12$ grade student. Kindly help me solve dis hard problem. Thank you.

Define the event $D$ as "Declared faulty" and the event $F$ as that a computer is faulty. By law of total probability

$$ P(D) = P(D\mid F)P(F) + P(D \mid F^c)P(F^c) $$ We know that they give the correct answer with probability $y$ so $P(D \mid F)=y$ and $P(D\mid F^c)=1-y$. Also we know $P(F)=x$ and $P(F^c)=1-x$ so it remains to put everything together.