Ok, here is a GRE question I cannot seem to solve. My coworker and I keep getting a negative number.
Of three possible events, event A is independent of the other two, and events B and C are mutually exclusive. The probabilities that the individual events A, B, and C will occur are 0.5, 0.3, and 0.2, respectively. What is the probability that both event A and event C will occur?
Can you please help? Thank you.
Edit: Thanks for your answers. The original wording was the following:
Of three possible events, events A and B are independent, and events B and C are mutually exclusive. The probabilities that the individual events A, B, and C will occur are 0.5, 0.3, and 0.2, respectively. What is the probability that both event A and event C will occur?
I believe they had realized the original question had a problem and fixed it. I was not aware of it when I posted this question.
Best Answer
Independence means that $$P(A|C)=\frac{P(A\cap C)}{P(C)}=P(A)$$ $$\implies P(A\cap C)=P(A)P(C)$$
I.e, the probability of $A$ occurring wasn't affected by the prior occurrence of $C$. So the probability that $A$ and $C$ will occur (which is $P(A\cap C)$) is $$P(A)P(C)=0.2\cdot 0.5=0.1$$