Final answer:
The sample space of spinning a fair spinner with numbers 1 to 4 and rolling a fair dice with numbers 1 to 6 is the set of all ordered pairs (spinner outcome, dice outcome), totaling 24 outcomes.
Step-by-step explanation:
The game involves spinning a fair spinner with numbers 1 to 4 and rolling a fair dice with numbers 1 to 6. To describe the sample space for this combined experiment, you will list all possible outcomes of both the spinner and the dice. Since there are four possible outcomes on the spinner and six on the dice, the total number of outcomes in the sample space will be 4 (from the spinner) times 6 (from the dice), which is 24 outcomes.
The sample space can be represented by an ordered pair (s, d) where s represents the outcome of the spinner and d represents the outcome of the dice. Therefore, the sample space S can be represented as:
- (1, 1)
- (1, 2)
- (1, 3)
- (1, 4)
- (1, 5)
- (1, 6)
- (2, 1)
- ...
- (4, 5)
- (4, 6)
Each pair represents one of the 24 possible outcomes when you spin the spinner and roll the dice during the game.