Machine M₁ makes 60% of a factory's pens and machine M₂ the rest; 2% of M₁'s pens and 3% of M₂'s are defective. A pen picked at random is defective. What is the probability that M₂ made it?

Conditional Probability & Bayes' Theorem · Question 117 of 125

Question 117

HardOriginal question

Machine $M_1$ makes 60% of a factory's pens and machine $M_2$ the rest; 2% of $M_1$ 's pens and 3% of $M_2$ 's are defective. A pen picked at random is defective. What is the probability that $M_2$ made it?

0.03

Correct answerYour answer

0.4

Correct answerYour answer

0.5

Correct answerYour answer

0.6

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Worth noting

0.4 is $M_2$ 's share of all pens; its higher defect rate lifts its share of defective pens to a half.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.