A faulty chip, which supplier shipped it?

Question

A phone maker sources chips from three suppliers. Supplier X provides $60\%$ of the chips with a $1\%$ fault rate. Supplier Y provides $30\%$ with a $2\%$ fault rate. Supplier Z provides $10\%$ with a $4\%$ fault rate. A chip pulled at random turns out faulty.

What is the probability it came from Supplier X?

Accepted Answer

Imagine 1{,}000 chips and count the faulty ones from each supplier. - Supplier X: 600 chips, 1\% faulty = 6. - Supplier Y: 300 chips, 2\% faulty = 6. - Supplier Z: 100 chips, 4\% faulty = 4. Total faulty chips: 6 + 6 + 4 = 16. Of these, 6 came from Supplier X: P(	ext{X} \mid 	ext{faulty}) = \frac{6}{16} = \frac{3}{8} = 0.375. Supplier X has the best quality yet the largest volume, so it ties for the most faults in absolute terms. Takeaway. A low fault rate does not clear a high-volume supplier; the count of defects depends on volume times rate.

A faulty chip, which supplier shipped it?

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