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From a bag of t red and 2 blue balls, two are drawn without replacement. Given the first is red, find the probability the second is blue.

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=6

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

After a red draw, total=t+1 and blue=2.

Worked solution

The requested value is 0.285714285714.

Checks and common pitfalls: The color count and denominator must reflect the information already given.

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.