Imagine rolling a six sided die, the sample space isa. {1, 2, 3, 4}b. {1, 2, 3, 4, 6}c. {1, 2, 3, 4, 5, 6}d. {1, 2}

Break Down the Problem

1. We need to determine the correct sample space when rolling a six-sided die.
2. A six-sided die can land on one of the numbers from 1 to 6.

Relevant Concepts

The sample space of an experiment is the set of all possible outcomes. For a standard six-sided die, the outcomes are represented as the numbers 1 through 6.

Analysis and Detail

1. The outcomes when rolling a six-sided die are:

   • 1 (first face)
   • 2 (second face)
   • 3 (third face)
   • 4 (fourth face)
   • 5 (fifth face)
   • 6 (sixth face)

2. Now we analyze the given options:

   • (a) {1, 2, 3, 4} - Incomplete, does not include 5 or 6.
   • (b) {1, 2, 3, 4, 6} - Incomplete, does not include 5.
   • (c) {1, 2, 3, 4, 5, 6} - Complete, includes all numbers from 1 to 6.
   • (d) {1, 2} - Incomplete, does not include 3, 4, 5, or 6.

Verify and Summarize

The only option that includes all possible outcomes of rolling a six-sided die without any omissions is option (c).

Final Answer

The correct sample space for rolling a six-sided die is (c) {1, 2, 3, 4, 5, 6}.