easy Probability

True Equation

A release-checked easy problem for training Combinations and Permutations, Dice.

Question

Dan has a fair $6$-sided die with faces labeled $1,2,3,4,+,$ and $-.$ In order to complete the equation \[ \underline{\qquad} \ \underline{\qquad} \ \underline{\qquad}=\underline{\qquad}, \] Dan repeatedly rolls his die and fills in a blank with the character he obtained, starting with the leftmost blank and progressing rightward. Find the probability that, when all blanks are filled, Dan forms a true equation.

Practice focus

This Probability problem is tagged Combinations and Permutations, Dice. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.