1. The problem statement, all variables and given/known data 1000 independent rolls of a fair die will be made. Compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively. If the number 6 appears exactly 200 times, find the probability that the number 5 will appear less than 150 times. 3. The attempt at a solution I have the first part correct. For the second part, I said: If X is the number of times a 6 appears and Y is the number of times a 5 appears, then we want P(Y<150|X=200). I simplified this to P(X=200 and Y<150)/(P(X=200), from which I could compute P(X=200). Since X and Y are not independent, I can't split the intersection up. I thought about rearranging the numerator into something involving a conditional probability (i.e like P(X=200 and Y<150) = P(X=200|Y<150)P(Y<150)) but I don't see how this helps.) I also noticed that this intersection looked like a joint RV, but I don't have the density function to do the necessary integration. Any advice on how to compute P(X=200 and Y<150)?