Dice Rolls – Max and Min

Suppose two 4-sided dice are rolled. Find the probabilities of the following events:

1. the maximum of the two numbers rolled is less than or equal to 2;
2. the maximum of the two numbers rolled is less than or equal to 3;
3. the maximum of the two numbers rolled is equal to 3;
4. Repeat part c for the maximum equal to 1, 2, and 4.
5. If M is the maximum of the two numbers, then

\[\mathbf{P}(M = 1) + \mathbf{P}(M = 2) + \mathbf{P}(M = 3) + \mathbf{P}(M = 4) = 1 \]

check that your answers for 3) and 5) satisfy this relationship.