Machine $X$ produces $70\%$ of a factory’s items; machine $Y$ produces $30\%$. Of

Question

Machine $X$ produces $70\%$ of a factory’s items; machine $Y$ produces $30\%$. Of $X$’s items, $2\%$ are defective. Of $Y$’s items, $5\%$ are defective. Draw a tree diagram with source first and defect status second. Find the probability that a randomly chosen item is defective. Given that an item is defective, find the probability that it came from $Y$.

Accepted Answer

(a) Tree branches below. (b) $0.029$. (c) $\frac{15}{29}$.

Probability

Probability

Solution:

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