Final answer:
The student is asked to list all events of an experiment with a sample space S = {5, 6, 15}, determine subsets containing 15, and subsets containing the number 6 or 15. There are a total of 8 possible events. There are 4 subsets containing the number 15, and there are 6 subsets that contain the number 6 or 15.
Step-by-step explanation:
The student is working on a probability problem involving the calculation of various events and their probabilities from a given sample space. In particular, the student needs to calculate events, the number of subsets containing certain numbers, and probabilities associated with these events.
Let S = {5, 6, 15} be the sample space of all outcomes from an experiment. The possible events from this sample space are:
- ∅ (the empty set)
- {5}
- {6}
- {15}
- {5, 6}
- {5, 15}
- {6, 15}
- {5, 6, 15} (the sample space itself)
To answer part (b) of the question, the number of subsets of S that contain the number 15 are 4, which are {15}, {5, 15}, {6, 15}, and {5, 6, 15}.
To answer part (c), the number of subsets of S that contain the number 6 or the number 15 are 6. These subsets include {6}, {15}, {5, 6}, {6, 15}, {5, 15}, and {5, 6, 15}.