Probability: Sample Space and Events
Question: A die is thrown. If A is an event of getting an odd number, then write the sample space and event A in set notation.
Solution & Explanation:
When a standard six-sided die is thrown, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6. In probability, this complete set of all possible outcomes is called the sample space, commonly denoted by the letter $S$.
Writing the sample space in set notation, we get:
$$S = \{1, 2, 3, 4, 5, 6\}$$
The problem defines Event A as the event of "getting an odd number". An odd number is any integer that cannot be divided exactly by 2.
By looking at our sample space $S$, we need to select only the numbers that are odd. Those numbers are 1, 3, and 5.
Writing Event A in set notation, we get:
$$A = \{1, 3, 5\}$$