Give a real-life example of the following: Exhaustive Events.

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Accepted Answer

> [!TLDR]
> Exhaustive events are events whose union equals the whole sample space — demonstrated using the roll of a single die.

> [!FORMULA]
> Events $A_1,A_2,\dots,A_n$ defined on a sample space $S$ are said to be **exhaustive** if
> $$A_1\cup A_2\cup\dots\cup A_n=S$$
> i.e., collectively they account for every possible outcome of the experiment.

1. **Set up the experiment.** Roll a single fair die once. Sample space $S=\{1,2,3,4,5,6\}$.
2. **Define the events.** Let $A=\{1,2,3\}$ ("the number is $\le 3$") and $B=\{4,5,6\}$ ("the number is $\ge 4$").
3. **Take the union.**
 $$A\cup B=\{1,2,3\}\cup\{4,5,6\}=\{1,2,3,4,5,6\}=S$$ …

Random Experiment	Sample Space
Toss a coin	$S = \{H, T\}$
Roll a die	$S = \{1, 2, 3, 4, 5, 6\}$
Toss two coins	$S = \{HH, HT, TH, TT\}$
Roll two dice	$S = \{(1,1), (1,2), \dots, (6,6)\}$ — 36 outcomes
Draw a card from a deck	$S = \{\text{A♠}, \text{K♠}, \dots, \text{2♣}\}$ — 52 outcomes

Q.Give a real-life example of the following: Exhaustive Events.

Concept understanding — Random Experiment and Sample Space

Random Experiment and Sample Space

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Examples to cement the idea

Q.Give a real-life example of the following: Exhaustive Events.

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