LEARN · EXPLAIN · REVISE

Events A,B are independent with P(A)=1/3 and P(B)=t/(t+1). Find P(A∩B).

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

高三選擇性必修第三册(A版).pdf · 7.1 · PDF 49 / printed page 44

TOPIC 01

Conditional and total probability

Use conditional denominators, disjoint partitions and Bayes inversion.

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

01 / Foundation#Your turn

t=7

The conditioning event must have positive probability; a total-probability partition is exhaustive and disjoint.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Express the event with a conditional probability or a disjoint partition.

Hint 2

Use this intermediate relation.

P(A\cap B)=P(A)P(B)

Worked solution

The requested value is 0.291666666667.

Checks and common pitfalls: Multiplication here is justified by the stated independence.

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

Teacher preparation and assessment

Defining relation: Use conditional denominators, disjoint partitions and Bayes inversion.
$P(A|B)=P(A\cap B)/P(B)$
Conditions: The conditioning event must have positive probability; a total-probability partition is exhaustive and disjoint.