Question

in a probability experiment using a cube numbered 1–6 and a spinner with three equal spaces, as shown. on each trial of the experiment, the number cube is tossed once and the arrow is spun once. what is the sample space for the experiment? a 1a b 1a, 3b, 5c c 1a, 3a, 2b, 3a, 3b, 3c, 4a, 5a, 5b, 6a, 6b, 6c d 1a, 1b, 1c, 2a, 2b, 2c, 3a, 3b, 3c, 4a, 4b, 4c, 5a, 5b, 5c, 6a, 6b, 6c

Explanation:

Step1: Determine cube outcomes

The number cube has numbers 1–6, so possible outcomes: \(1, 2, 3, 4, 5, 6\).

Step2: Determine spinner outcomes

The spinner has 3 equal spaces: \(A, B, C\).

Step3: Find sample space

For each cube outcome (\(1 - 6\)), pair with each spinner outcome (\(A, B, C\)).
E.g., \(1\) pairs with \(A, B, C\) (\(1A, 1B, 1C\)), \(2\) pairs with \(A, B, C\) (\(2A, 2B, 2C\)), and so on for \(3 - 6\).
This gives all combinations: \(1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C, 4A, 4B, 4C, 5A, 5B, 5C, 6A, 6B, 6C\), matching option D.

Answer:

D. 1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C, 4A, 4B, 4C, 5A, 5B, 5C, 6A, 6B, 6C