4. How can you write the situation as a probability using symbols and variables? Use \( x \) for the variable. Do NOT use spaces in your answer. 4. What is the sample space? 5. How many possible outcomes are in the sample space? 6. How many favorable outcomes are in the sample space? not find the probability yet. How likely is it that Tucker will get a higher number than Rosette?

To express the situation as a probability using symbols and variables, you can denote that event of Tucker getting a higher number than Rosette as \( P(T>x) \), where \( T \) is Tucker's number and \( x \) is Rosette's number. This represents the likelihood of Tucker's outcome being greater than Rosette's. The sample space consists of all possible outcomes of their respective numbers. If we assume they each roll a die, the sample space would be \( \{(1,1), (1,2), (1,3), \ldots, (6,6)\} \), which includes all combinations of their rolls. For two six-sided dice, the sample space has 36 different pairs since each die has 6 faces. The sample space has 36 possible outcomes (as deduced from the six outcomes for Tucker and the six outcomes for Rosette combined). This means every combination of their rolls is accounted for, giving us that total of 36 unique pairs. Favorable outcomes refer to the instances where Tucker's number is higher than Rosette's. Without calculating the probability yet, if you track the pairs satisfying \( T > x \) (like (2,1), (3,1), (3,2), etc.), you will find there are 21 favorable outcomes in total.