Selecting a Bill A box contains a 1 bill, a 5 bill, a 10 bill, and a 20 bill.

step 1 A container has in it a one, a five, a ten, and a twenty dollar bill. We're going to select one

Selecting a Bill A box contains a 1 bill, a 5 bill,...

$$ \begin{array}{l}{\text { Selecting a Bill A box contains a } \$ 1 \text { bill, a } \$ 5 \text { bill, a }} \\ {\$ 10 \text { bill, and a } \$ 20 \text { bill. A bill is selected at random, and }} \\ {\text { it is not replaced; then a second bill is selected at random. }} \\ {\text { Draw a tree diagram and determine the sample space. }}\end{array} $$

$$
\begin{array}{l}{\text { Selecting a Bill A box contains a } \$ 1 \text { bill, a } \$ 5 \text { bill, a }} \\ {\$ 10 \text { bill, and a } \$ 20 \text { bill. A bill is selected at random, and }} \\ {\text { it is not replaced; then a second bill is selected at random. }} \\ {\text { Draw a tree diagram and determine the sample space. }}\end{array}
$$

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Key Concepts

Without Replacement

The concept of selecting items without replacement refers to the process where an item, once selected, is not returned to the set before the next selection occurs. This changes the composition of the remaining set, thereby affecting the probabilities of subsequent selections and often necessitating adjustments in counting the outcomes or recalculating conditional probabilities.

Sample Space

The sample space in probability is the complete set of all possible outcomes of an experiment. It serves as the foundational reference for assessing probabilities by enumerating every distinct outcome that can occur, thereby enabling the calculation of event probabilities through the ratio of favorable outcomes to the total number of outcomes.

Tree Diagram

A tree diagram is a visual tool used in probability to systematically display all possible outcomes of an event, especially those involving sequential choices or multiple steps. It branches out each decision point, allowing each subsequent outcome to be easily tracked, which helps in organizing and computing probabilities for complex experiments.

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