Complete the sample space shown in the table for the compound event of rolling a number cube and spinning a spinner that is split into three equally colored sections (red (R), blue (B), and yellow (Y)). Ensure the letter corresponding to the colored section of the spinner is capitalized in your responses.

Question

Complete the sample space shown in the table for the compound event of rolling a number cube and spinning a spinner that is split into three equally colored sections (red (R), blue (B), and yellow (Y)). Ensure the letter corresponding to the colored section of the spinner is capitalized in your responses.

Answer 1

The sample space for rolling a number cube and spinning a spinner is given by the set of all possible outcomes. Since there are 6 possible outcomes when rolling a number cube (1, 2, 3, 4, 5, 6) and 3 possible outcomes when spinning the spinner (R, B, Y), we can determine the sample space by listing all possible combinations of these outcomes:

{(1, R), (1, B), (1, Y),
(2, R), (2, B), (2, Y),
(3, R), (3, B), (3, Y),
(4, R), (4, B), (4, Y),
(5, R), (5, B), (5, Y),
(6, R), (6, B), (6, Y)}

Here, each element of the sample space is represented as a tuple, with the first element denoting the outcome of rolling the number cube and the second element denoting the outcome of spinning the spinner. The letter representing the color on the spinner is capitalized as requested.