Which table correctly displays all the possible outcomes for tossing a coin and rolling an even number on a six-sided die? 1. Coin | Die | Outcome - Heads | 2 | Heads, 2 - Heads | 4 | Heads, 4 - Heads | 6 | Heads, 6 - Tails | 2 | Tails, 2 - Tails | 4 | Tails, 4 - Tails | 6 | Tails, 6 The table above is the only one that correctly shows all the possible outcomes for the described scenario—tossing a coin and only rolling an even number on a six-sided die.

The given table correctly displays all the possible outcomes for tossing a coin and rolling an even number on a six-sided die. The coin has two possible outcomes: Heads or Tails. A six-sided die typically has three even number outcomes: 2, 4, and 6. This scenario leads to a total of 2 (coin outcomes) × 3 (even die outcomes) = 6 distinct and possible outcomes. Here is the table for reference:

Coin | Die | Outcome - Heads | 2 | Heads, 2 - Heads | 4 | Heads, 4 - Heads | 6 | Heads, 6 - Tails | 2 | Tails, 2 - Tails | 4 | Tails, 4 - Tails | 6 | Tails, 6

Each combination represents a unique outcome for the coin toss and die roll, covering all possible events for this specific situation.

Extra: When we deal with probability and outcomes, we often use the fundamental counting principle, which says that if you have one event that can occur in m ways and another independent event that can occur in n ways, then the total number of ways both events can occur is m × n.

In this case, the coin is an event with two outcomes (m = 2 for Heads and Tails) and the die rolls an even number as an event with three outcomes (n = 3 for the numbers 2, 4, and 6). Multiplying these gives us the six unique possible outcomes listed in the table.

It's important to note that each die roll is independent of the coin toss, and vice versa—meaning the outcome of one does not affect the outcome of the other. This is why we can calculate the total number of outcomes by simply multiplying the number of outcomes for each individual event.

Understanding these concepts is fundamental to tackling more complex problems in probability and combinatorics, which are branches of mathematics that deal with counting, arrangement, and occurrence of events.