Question

two standard six - sided dice are rolled. determine the set of outcomes for rolling a number less than 3 on both dice. ((1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)) ((1,1),(1,2),(2,1),(2,2)) ((1,2,3)) ((1,2))

Explanation:

Step1: List possible outcomes

When rolling two six - sided dice, each die has 6 possible values. We want values less than 3 (i.e., 1 and 2) on both dice. The possible pairs are formed by combining the values of the first die (1 or 2) with the values of the second die (1 or 2).

Step2: Generate pairs

The pairs are \((1,1)\), \((1,2)\), \((2,1)\), \((2,2)\). So the set of outcomes is \(\{(1,1),(1,2),(2,1),(2,2)\}\)

Answer:

\(\{(1,1),(1,2),(2,1),(2,2)\}\)