A loaded 6-sided die has probability 1/4 for 3 & 4 and 1/8 for 1,2,5,6. If i decide whether a die is loaded or not based on one roll what is the probability of falsely classifying a fair die as loaded? What is the probability of classifying a loaded die as fair?
Not sure how to solve this. The probability of getting a 3 or 4 on a loaded die is 1/2 and on a fair die it is 1/3. The likelihood ratio is 3/2. Where do i go from here?
You are going to classify a fair die as loaded if it lands on a $3$ or $4$.
$P(3,4) = \frac{1}{3}$
You are going to classify a loaded die as fair if it lands on $1,2,5$ or $6$
$P(1,2,5,6) = \frac{1}{2}$