LEARN · EXPLAIN · REVISE

P(A)=1/2,P(B)=1/3,P(A∩B)=1/(6k). Find P(A∪B).

Read the idea, work independently, then explain what changed.

高一必修第二册(A版).pdf · 10.1 · PDF 235 / printed page 228

TOPIC 01

Random events and probability

Build understanding of random events and probability through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

k=3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Describe the sample space and event sets, then count or apply a probability identity.

Hint 2

Subtract the intersection once.

Worked solution

Describe the sample space and event sets, then count or apply a probability identity.
Calculate or simplify this relation.
$P(A\cup B)=1/2+1/3-1/18$
The overlap was counted in both separate probabilities.

The requested value is 0.77777778.

Checks and common pitfalls: The overlap was counted in both separate probabilities.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use random events and probability to state a justified conclusion.
Event sets: An event is a subset of the sample space; probability is its numerical measure.
Probability rules: Use complements and inclusion-exclusion with their set meanings.
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Close with: conditions → representation → reasoning → check.

Expected reasoning: An event is a subset of the sample space; probability is its numerical measure.
Expected reasoning: Use complements and inclusion-exclusion with their set meanings.
Expected correction: Disjointness and independence describe different relationships.