Basic Probability UPCAT Reviewer: Lesson and Practice

TEACHER ABI UPCAT MATHEMATICS

Basic Probability

Define the event, count the equally likely outcomes, and choose whether to add, multiply, or complement.

5-10 minute lesson27 original questionsAdaptive practiceSaves progress

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Basic Probability

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Define the event and the sample space before calculating

For equally likely outcomes, probability is favorable outcomes divided by total outcomes. Use the complement for “not” or “at least one.” Independent events joined by “and” multiply. Without replacement, update the denominator because the first selection changes what remains.

P(E)=favorabletotalP(not E)=1−P(E)P(A and B)=P(A)P(B) for independent events

Range

Probability is from 0 to 1.

Language

“Not” suggests complement; independent “and” suggests multiplication.

DO IT FAST

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.

WORKED EXAMPLES

Five forms you should recognize

1. Single event

Five red counters among ten total give:

P(red)=510=12

2. Complement

If P(rain)=0.35:

P(no rain)=1−0.35=0.65

3. Independent events

For heads and an even die result:

P=12·36=14

4. Without replacement

From 3 red and 2 blue counters, drawing two red without replacement:

P=35·24=310

5. At least one

For two coin tosses, use the complement of no heads:

P(at least one head)=1−P(TT)=1−14=34

COMMON TRAPS

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

FIVE-FORM SKILL CHECK

Do you need the lesson-or just practice?

One original question in each form recommends your next step. It does not yet verify mastery.

CHOOSE YOUR PRACTICE

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.

FRESH MASTERY CHECK

Ready to verify this competency?

A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.

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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.

RELATED COMPETENCIES

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