Question:
Two sources output a number at equal rates. The output from source A is uniformly distributed between 100 and 199, and the output from source B is uniformly distributed between 50 and 249. If the number 125 is output, what is the probability that it came from source A?
I'm assuming I need to look at the pdf of each source, but I'm not sure if I have to form some sort of joint probability function. Any help/hints are appreciated.
Best Answer
Hint:
You need to find $P(\text{The number came from source } A|\text{The number is } 125)$. You have $P(\text{The number is }x|\text{The number came from source } A)$ and $P(\text{The number is }x|\text{The number came from source } B)$.
Also I think "Two sources output a number at equal rates." may mean $P(\text{The number came from source } B)=P(\text{The number came from source } A)$.
Now use Bayes rule.