A quality control analyst inspected a batch of 180 microchips from two production lines, Line A and Line B. The microchips were classified as Defective, Acceptable, or Premium. Some of the data from the inspection are shown in the table below.
| Production Line | Defective | Acceptable | Premium | Total |
|---|---|---|---|---|
| Line A | 10 | 50 | ||
| Line B | 15 | 35 | ||
| Total | 25 | 55 | 180 |
If a microchip is selected at random from those classified as Defective or Premium, what is the probability that the chip was produced by Line A?
Cevap: 0.375
Cevap
The correct answer is 3/8 (or 0.375).
To find the probability that a randomly selected microchip was produced by Line A given that it is classified as Defective or Premium, we restrict the sample space to only the Defective and Premium microchips. From the table, the total number of Defective microchips is 25, and the total number of Premium microchips is 55, giving a combined group size of 25 + 55 = 80 microchips. Next, we determine how many of these 80 microchips were produced by Line A. Line A produced 10 Defective microchips and x Premium microchips. Since the total number of Premium microchips is 55 and Line B produced 35, Line A produced x = 55 - 35 = 20 Premium microchips. Thus, the number of microchips produced by Line A that are Defective or Premium is 10 + 20 = 30. The conditional probability is the number of favorable outcomes divided by the restricted total outcomes, which is 30/80 = 3/8 (or 0.375).
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Conditional Probability from Two-Way Tables
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