1. Pr(P=It takes state s_6 | Q as stated) = 1/6. (Q - "must take one of 6 states" implies this is a fair die, no other outcomes are possible.
2. Pr(P | Q & “fair die”) = 1/6; "fair die" is an irrelevant addition since the definition of Q excludes any other possible outcome than 1 through 6.
3. If "must take one of 6 states" is excluded from the definition of Q, then we may not have a fair die, so there may be a 7th state which is not 1 through 6. In which case Pr(P=It takes state s_6 | Q as stated) = 1/7.
So, my attempt at the homework:
1. Pr(P=It takes state s_6 | Q as stated) = 1/6. (Q - "must take one of 6 states" implies this is a fair die, no other outcomes are possible.
2. Pr(P | Q & “fair die”) = 1/6; "fair die" is an irrelevant addition since the definition of Q excludes any other possible outcome than 1 through 6.
3. If "must take one of 6 states" is excluded from the definition of Q, then we may not have a fair die, so there may be a 7th state which is not 1 through 6. In which case Pr(P=It takes state s_6 | Q as stated) = 1/7.
How am I doing?