Compound Event
In short: Compound event describes a result built from two or more simple events, like a spin plus a flip, and its probability counts only outcomes where every part happens together.
7th GradeProbability7.SP.C.8a
What is Compound Event?
A compound event asks about more than one thing at once: the spinner lands on gold and the coin shows tails, or a card is red or a face card. Each piece is a simple event; the combination is the compound one.
When the stages do not influence each other, probabilities multiply: \(P(A \text{ and } B) = P(A) \times P(B)\). To count the outcomes directly, build the sample space with a table, an organized list or a tree and mark every outcome that fits.
How to spot it
- A problem joins two actions, like a coin toss with a spin, two dice rolls, or two cards drawn.
- The wording uses and or or to link two conditions on the same trial.
- You must find the chance that two separate things both happen.
- A table or tree is drawn so that all combinations can be marked.
The method
- Identify each simple event and state its probability separately.
- Decide whether one stage changes the other; if not, they are independent.
- For independent stages joined by and, multiply the probabilities; list the outcomes if counting is clearer.
- Simplify the product and, if asked, convert it to a percent.
Compound Event: solved example
Problem
A school carnival wheel has 5 equal sections: 2 gold and 3 gray. A player spins the wheel and also flips a coin. What is the probability of gold and tails?
Solution
The wheel and the coin do not affect each other. \(P(\text{gold}) = \frac{2}{5}\) and \(P(\text{tails}) = \frac{1}{2}\).
Multiply: \(\frac{2}{5} \times \frac{1}{2} = \frac{2}{10} = \frac{1}{5}\). The chance is \(\frac{1}{5}\), or 20%.
Try it
Question 1
Two balanced cubes are tossed together. How likely is a total of 7?
Show the answer
Of the 36 equally likely ordered pairs, exactly 6 add to 7, so the chance is \(\frac{6}{36} = \frac{1}{6}\).
Question 2
A balanced nickel lands three times in a row. How likely is heads on every landing?
Show the answer
\(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}\).
Compound Event vs. Sample Space
A compound event is the combination you are asking about, such as gold and tails. The sample space is the full list of results from which the combination is picked. Count the compound event’s outcomes for the top of the fraction, and the whole space for the bottom.
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Related words
Whole dictionary: A–Z · 7th Grade · Probability