Let S = {2, 8, 14} be a sample space associated with an experiment.
(a) List all events of this experiment.
A) {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
B) {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}
C) {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}, {2, 8, D) 14}
E) ∅, {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}
F) ∅, {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
G) ∅, {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
(b) How many subsets of S contain the number 14?
(c) How many subsets of S contain either the number 8 or the number 14?
Nvm, I got it! Thanks anyway
To answer the questions, we need to understand what a sample space and events are in the context of an experiment.
In probability theory, a sample space (denoted as S) represents the set of all possible outcomes of an experiment. An event is any subset of the sample space, meaning it is a collection of possible outcomes of the experiment.
(a) To list all events of the experiment, we need to find all possible subsets of the given sample space {2, 8, 14}.
Using the concept of combinations, we can find the subsets by considering each element individually, and then combinations of pairs, triplets, and the full set.
The possible events are:
A) {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
B) {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}
C) {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
E) ∅, {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}
F) ∅, {2}, {8}, {14}, {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
G) ∅, {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
(b) To find the subsets that contain the number 14, we need to consider only those events that include the element 14. From the list of events:
A) {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
There are four such subsets.
(c) To find the subsets that contain either the number 8 or the number 14, we need to consider events that contain at least one of these elements. From the list of events:
A) {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
B) {8}, {14}, {2, 8}, {2, 14}, {8, 14}
C) {8}, {14}, {2, 8}, {2, 14}, {8, 14}, {2, 8, 14}
There are six such subsets.