Pre-Algebra
Probability (introductory)
Probability of simple events
20 practice questions
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Theory + worked examples
Probability of Simple Events
Texas Pre-Algebra (TEKS) • Standard 7.6(E) • Probability
Probability of Simple Events is the opening topic of Probability in the Texas Essential Knowledge and Skills. It is aligned to Standard 7.6(E), which requires students to find the probability of simple events.
The probability of a simple event is the number of favorable outcomes over the total, always between \(0\) and \(1\).
Theory
The probability of an event is the number of favorable outcomes divided by the total number of equally likely outcomes.
\(0\le P\le1\): \(0\) is impossible, \(1\) is certain.
The probability scale.
Simple probability.
Probability:
\[P(\text{event})=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}\]
The complement: \(P(\text{not }A)=1-P(A)\).
How to find a probability
- Count the favorable outcomes.
- Count the total equally likely outcomes.
- Divide favorable by total.
- Simplify the fraction.
Example 1 — A die
Find \(P(\text{rolling a }4)\) on a fair die.
Solution
One favorable of six.
| \(P\) | \(=\) | \(\dfrac{1}{6}\) |
Example 2 — Even number
Find \(P(\text{even})\) on a die.
Solution
Three favorable \((2,4,6)\).
| \(\dfrac{3}{6}\) | \(=\) | \(\dfrac{1}{2}\) |
Example 3 — Spinner
A spinner has \(4\) equal parts, \(1\) red. Find \(P(\text{red})\).
Solution
One of four.
| \(P\) | \(=\) | \(\dfrac{1}{4}\) |
Example 4 — Complement
If \(P(\text{win})=0.3\), find \(P(\text{not win})\).
Solution
Subtract from \(1\).
| \(1-0.3\) | \(=\) | \(0.7\) |
Common pitfalls
Probability is between \(0\) and \(1\).
Outcomes must be equally likely.
The complement is \(1-P\).
Frequently asked questions
How do I find probability?
Favorable outcomes divided by total outcomes.
What is the range of probability?
From 0 to 1.
\(P\) of rolling a 4?
\(\dfrac16\).
What is the complement?
\(1-P\).
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Experimental vs. theoretical probability
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