LEARN · EXPLAIN · REVISE

Choose machine 1 with probability 1/(t+2), otherwise machine 2; their failure rates are 1/10 and 1/5. Given failure, find P(machine 1).

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 / Standard#Your turn

t=30

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(M_1|F)=P(M_1\cap F)/P(F)

Worked solution

Express the event with a conditional probability or a disjoint partition.
Apply the stated relation and retain its conditions.
$P(F)=63/[10(32)]$
Apply the stated relation and retain its conditions.
$P(M_1|F)=\frac{1/[10(32)]}{63/[10(32)]}=1/63$
The posterior denominator includes failures from both machines.

The requested value is 0.015873015873.

Checks and common pitfalls: The posterior denominator includes failures from both machines.

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

Teacher preparation and assessment