LEARN · EXPLAIN · REVISE

A fair coin selects a bag: bag 1 has t red and 1 blue; bag 2 has 1 red and t blue. Given a red draw, find the probability bag 1 was chosen.

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 / Transfer#Your turn

t=14

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 Bayes with P(red)=1/2.

Worked solution

Express the event with a conditional probability or a disjoint partition.
Apply the stated relation and retain its conditions.
$P(R)=\tfrac12[t/(15)+1/(15)]=1/2$
Apply the stated relation and retain its conditions.
$P(B_1|R)=t/15$
Equal bag-selection priors do not remain equal after observing the color.

The requested value is 0.933333333333.

Checks and common pitfalls: Equal bag-selection priors do not remain equal after observing the color.

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.