LEARN · EXPLAIN · REVISE

Independent trials succeed with probability 1/2. Find the least n for success at least once with probability ≥1−2^(−m).

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

TOPIC 01

Random variables and distributions: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

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

01 / Transfer#Your turn

m=3

Binomial trials have fixed n, common p and independence; hypergeometric sampling uses a finite population without replacement.

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.

1-2^{-n}\ge1-2^{-m}

Worked solution

Express the event with a conditional probability or a disjoint partition.
Apply the stated relation and retain its conditions.
$2^{-n}\le2^{-3}\Rightarrow n\ge3$
Use the complementary event of no successes.

The requested value is 3.

Checks and common pitfalls: Use the complementary event of no successes.

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

Teacher preparation and assessment