The table gives the proportions of microchips that a certain PC manufacturer purchases from seven suppliers.
Supplier ---------- Proportion
S1 ---------------- 0.15
S2 ---------------- 0.05
S3 ---------------- 0.10
S4 ---------------- 0.20
S5 ---------------- 0.12
S6 ---------------- 0.20
S7 ---------------- 0.18
a)It is known that the proportions of defective microchips produced by the seven suppliers are 0.001, 0.0003, 0.0007, 0.006, 0.0002, 0.0002 and 0.001 respectively. If a single PC microchip failure is observed, which supplier is most likely responsible?
b) Suppose the seven suppliers produce defective microchips at the same rate, 0.0005. If a single PC microchip failure is observed, which supplier is most likely responsible?
Any idea? It seems simple to me buy my lecturer said that we have to think hard for this question. Is it a trick question or smtg? Ty.
Answers & Comments
Start working backward: if the probability of a defective chip is equal across all manufacturers, then the manufacturer that supplies the most chips is most likely to be the source of the defective chip, so the answer for Part (b) is that it is equally likely to be Supplier 4 or Supplier 6, since they supplied the same number of chips and the largest number.
For Part (a), you need a weighted average: the chances of a defective chip from a manufacturer will be the product of the proportion of chips they provide with the probability that any given chip of their is defective.
I'm not gonna do *all* your homework for you... I'd suggest making a spreadsheet in Excel (or a similar program) with the two columns you have already plus a third column for the probabilities and a fourth for the products. Largest product (they'll all be small numbers) is most likely to be the source of a defective chip.
(My best guess by eye, without doing all the calculations, is that S4 is the culprit... ;-) )
There are lies, damned lies, and statistics