Printers X, Y and Z print 30%, 45% and 25% of…

Printers X, Y and Z print 30%, 45% and 25% of an office's pages, and 2%, 4% and 6% of their pages,…

Question 111

MediumOriginal question

Printers $X$ , $Y$ and $Z$ print 30%, 45% and 25% of an office's pages, and 2%, 4% and 6% of their pages, respectively, are smudged. A page is picked at random, and $S$ is the event that it is smudged. Match each probability in List I with its value in List II.

List I	List II
A. $P(S)$	I. $\frac{2}{13}$
B. $P(X \mid S)$	II. $\frac{5}{13}$
C. $P(Y \mid S)$	III. $0.039$
D. $P(Z \mid S)$	IV. $\frac{6}{13}$

A-III, B-I, C-IV, D-IICorrect answerYour answerA-III, B-IV, C-I, D-IICorrect answerYour answerA-III, B-I, C-II, D-IVCorrect answerYour answerA-III, B-II, C-IV, D-ICorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

$P(S) = 0.3 \times 0.02 + 0.45 \times 0.04 + 0.25 \times 0.06 = 0.006 + 0.018 + 0.015 = 0.039$ .
$P(X \mid S) = \frac{6}{39} = \frac{2}{13}$ , $P(Y \mid S) = \frac{18}{39} = \frac{6}{13}$ and $P(Z \mid S) = \frac{15}{39} = \frac{5}{13}$ .

Worth noting

The three printers' chances add to 1, since a smudged page came from exactly one of them.

Concept: Bayes' theorem with three hypotheses
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsBayes' theorem

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

Practise this chapter →

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

Printers X, Y and Z print 30%, 45% and 25% of an office's pages, and 2%, 4% and 6% of their pages,…

Question 111

Explanation