Question 2

A sample space lists all possible outcomes of an experiment.

Step 1 — Outcomes for die and coin

Let's list the outcomes for rolling a die. The die can show 1, 2, 3, 4, 5, or 6. Let's list the outcomes for tossing a coin. The coin can show Heads (H) or Tails (T).

Step 2 — Combine outcomes for (i)

We combine each die outcome with each coin outcome. Each combined outcome is a pair. The first element is the die result. The second element is the coin result. The sample space S is: $S = \{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)\}$ The total number of outcomes is 12.

$\boxed{S = \{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)\}}$

Step 3 — Identify integers for (ii)

We need to find all integers. These integers are between -5 and +5. This includes both -5 and +5. Let's list them in order. The sample space S is: $S = \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}$ The total number of outcomes is 11.

$\boxed{S = \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}}$

Step 4 — Consider ball types for (iii)

We have two types of balls. There are green (G) balls. There are red (R) balls. We draw only one ball. The outcome is the color of the ball. The sample space S is: $S = \{G, R\}$ The total number of outcomes is 2.

$\boxed{S = \{G, R\}}$

Step 5 — Note on distinguishable balls

Sometimes, individual balls are considered unique. For example, $G_1, G_2, ..., G_5$ and $R_1, R_2, ..., R_7$. This would give 12 distinct outcomes. However, for probability at this level, we use the color-based space.

Answer

(i) $S = \{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)\}$ (ii) $S = \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}$ (iii) $S = \{G, R\}$