Discrete Probability - error with question?
1. The problem statement, all variables and given/known data
On a long train journey, a statistician is invited by a gambler to play a dice game. The game uses 2 unbiased ordinary dice which the statistician is to throw. If the total score is 12, the statistician is paid 3 dollars by the gambler. However,if both or either dice show a '1', the statistician pays the gambler 2 dollars.
Let X= amount paid to the statistician by the gambler after the dice are thrown once.
Determine the probability that X=6,X=3 and X=-2.
I have one question...how do we determine the probability that X=6 since the question states that the statistician is paid 3 dollars by the gambler if the total score is 12 and X is the amount paid to the statistician after the dice are thrown once?
There's an error with the question isn't it? I need a second opinion on this. Thank you.