You and your friend are playing a game with two number cubes. If you roll doubles or two numbers that are both even, you get to take another turn and roll again. Which of the following options is a subset for either rolling doubles or both numbers being even?

Answer 1

To determine a subset of the outcomes where you either roll doubles or both numbers are even, we can first clarify the conditions:

1. Doubles: This occurs when both dice show the same number. For two six-sided dice, the possible outcomes for doubles are:

   • (1,1)
   • (2,2)
   • (3,3)
   • (4,4)
   • (5,5)
   • (6,6)

2. Both numbers are even: The even numbers on a six-sided die are 2, 4, and 6. The possible outcomes when both dice roll even numbers are:

   • (2,2)
   • (2,4)
   • (2,6)
   • (4,2)
   • (4,4)
   • (4,6)
   • (6,2)
   • (6,4)
   • (6,6)

Now, we can list the outcomes that satisfy either condition:

• Doubles: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
• Even number combinations: (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6)

Let's combine these outcomes to find the total events of either rolling doubles or both numbers being even:

• (1,1) (From doubles)
• (2,2) (From doubles and even)
• (2,4) (From even)
• (2,6) (From even)
• (3,3) (From doubles)
• (4,2) (From even)
• (4,4) (From doubles and even)
• (4,6) (From even)
• (5,5) (From doubles)
• (6,2) (From even)
• (6,4) (From even)
• (6,6) (From doubles and even)

Now we compile the unique outcomes:

1. (1,1)
2. (2,2)
3. (2,4)
4. (2,6)
5. (3,3)
6. (4,2)
7. (4,4)
8. (4,6)
9. (5,5)
10. (6,2)
11. (6,4)
12. (6,6)

The complete combination of outcomes is:

• (1,1), (2,2), (2,4), (2,6), (3,3), (4,2), (4,4), (4,6), (5,5), (6,2), (6,4), (6,6)

Now, any subset of these outcomes would qualify as a possible option for rolling doubles or both numbers being even in the game context you described.

If you need options to choose from or specific subsets containing certain elements, please provide them, and we can find the appropriate subset together!