Solve simple compound-event problems

Compound-event probability describes the likelihood of an event formed from two or more outcomes or stages, such as getting a particular color and number or selecting one result or another. Learners represent the complete sample space with organized lists, tables, or tree diagrams, count equally likely outcomes, and combine favorable outcomes without double-counting overlapping cases, expressing probabilities as fractions, decimals, or percents; conditional probability and more general dependent-event formulas are beyond this level.

Detailed Explanation: Solve simple compound-event problems

A compound event combines two or more parts. To find its probability:

List all possible outcomes.
Count the outcomes that match the event.
Write

\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}.

Example

A spinner has three equal sections: red, blue, and green. You also roll a fair number cube labeled $1$ through $4$ .

What is the probability of getting red and an even number, or blue and $1$ ?

Step 1: List the complete sample space

Each color can be paired with each number:

Color	Possible numbers
Red	$1,2,3,4$
Blue	$1,2,3,4$
Green	$1,2,3,4$

There are $3 \times 4=12$ equally likely outcomes.

Step 2: Find the favorable outcomes

Red and an even number: $(\text{red},2)$ and $(\text{red},4)$
Blue and $1$ : $(\text{blue},1)$

So there are $3$ favorable outcomes.

Step 3: Find the probability

P=\frac{3}{12}=\frac{1}{4}

The probability is $\boxed{\frac14}$ , or $25\%$ .

When combining outcomes, list each favorable outcome only once. This prevents double-counting.

Learn by doing: Solve simple compound-event problems

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Probability - Shapes, Two Sets of Two Shapes, Two Colors - Pick Two by Color, To Fraction

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