Final answer:
The number of possible outcomes when rolling a six-sided die and drawing a token from a bag with three pink and one red is 24. These outcomes are the product of multiplying the 6 outcomes of the die by the 4 outcomes of the token draw. The outcomes can be listed systematically, combining each die result with each token color.
Step-by-step explanation:
To find the number of possible outcomes in our sample space for rolling a die and drawing a token from a bag containing three pink tokens and one red token, we first count the outcomes from each activity and then multiply these numbers together. Rolling a fair six-sided die yields a sample space of {1, 2, 3, 4, 5, 6} which has 6 possible outcomes. Drawing a token from the bag gives us 4 possible outcomes: 3 pink (P1, P2, P3 for distinction) and 1 red (R).
- Die roll: 6 outcomes
- Token draw: 4 outcomes
Multiplying the number of outcomes for the die and the token draw, 6 outcomes from the die roll multiplied by 4 outcomes from the token draw, gives us a total of 24 possible outcomes in the sample space.
The possible outcomes can be systematically listed as follows, where the first number denotes the die roll and the second letter denotes the token color:
- 1P1, 1P2, 1P3, 1R
- 2P1, 2P2, 2P3, 2R
- 3P1, 3P2, 3P3, 3R
- 4P1, 4P2, 4P3, 4R
- 5P1, 5P2, 5P3, 5R
- 6P1, 6P2, 6P3, 6R