Basic Probability
Define the event, count the equally likely outcomes, and choose whether to add, multiply, or complement.
Basic Probability
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Probability compares favorable outcomes with all possible outcomes
For equally likely outcomes, P(event)=favorable outcomes ÷ total outcomes. A complement uses 1−P(event). Independent events joined by “and” multiply.
Range
Probability is from 0 to 1.
Language
“Not” suggests complement; independent “and” suggests multiplication.
Translate the event before choosing an operation
Problem: A fair coin is tossed and a fair six-sided die is rolled. What is the probability of getting heads and a 1?
Recognize: Two independent events must both happen. Heads has probability 12; rolling 1 has probability 16.
Do it fast: For independent events joined by “and,” multiply: 12×16=112.
If the question instead asked for not heads, use the complement: 1−P(heads)=12.
Why it works
Writing the required event in words reveals the structure: favorable over total for one stage, complement for “not,” and multiplication for independent events that must both occur.
Five forms you should recognize
3 red among 10 counters gives 310.
If P(rain)=0.3, P(no rain)=0.7.
Heads and a 1 on a six-sided die: 12×16=112.
8 wins in 20 games estimates 820.
With equally likely cards, the larger count is more likely.
Check before you commit
- Dividing by the wrong total
- Adding probabilities for an “and” event
- Forgetting replacement conditions
- Treating observed frequency as certainty
- Using counts when outcomes are not equally likely
- Leaving probability above 1
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Basic Probability FAQ
Why are there two mastery sets?
A different five-question set appears after an unsuccessful attempt so memorizing one set does not verify mastery.
Does 5/5 mean I never need this topic again?
It verifies this competency today; revisit it later through mixed practice.
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