Jo flips a coin {H, T}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}.

Question

Which of the following outcomes are in the sample space of this experiment?

Answer 1

In this experiment, Jo performs two actions: flipping a coin and rolling a 6-sided die. Therefore, the sample space consists of all possible combinations of outcomes from these two actions.

1. The outcomes from flipping the coin can be either Heads (H) or Tails (T).
2. The outcomes from rolling the die can be any of the numbers: 1, 2, 3, 4, 5, or 6.

To construct the sample space, we combine each outcome from the coin flip with each outcome from rolling the die. This results in the following outcomes:

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

Thus, the complete sample space includes 12 outcomes:

{ (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) }

You can now check specific outcomes against this list to see if they belong to the sample space.