Answer:

Certainly! The sample space represents the set of all possible outcomes for an experiment. Here are the sample spaces for the provided scenarios:

a) **Losing two coins at once:**

- When losing two coins at once, the possible outcomes would be:

\{ (Heads, Heads), (Heads, Tails), (Tails, Heads), (Tails, Tails) \}

b) **Tossing a coin 4 times:**

- When tossing a coin 4 times, the sample space consists of all possible combinations of heads (H) and tails (T) in four tosses.

Sample space: \{ HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, THTH, HTTH, TTHT, TTHH, TTTT, TTTH, TTHT, HTTT \}

c) **Spinning a spinner with five colors:**

- When spinning a spinner with five colors (red, green, orange, yellow, blue), the sample space would be:

Sample space: \{ Red, Green, Orange, Yellow, Blue \}

d) **Rolling two dice simultaneously:**

- Rolling two dice simultaneously would have a sample space consisting of all possible combinations of numbers on each die. Each die can show numbers from 1 to 6.

Sample space:

\{ (1, 1), (1, 2), (1, 3), ..., (1, 6), (2, 1), (2, 2), ..., (6, 5), (6, 6) \}

These sample spaces represent the exhaustive list of all possible outcomes for each of the scenarios described.