Concept explainers
In Exercises 1–22, use Bayes’ theorem to calculate the probabilities.
Quality Control A scoreboard has six different types of LEDs. For each type of LED, Table 3 gives the proportion of the total number of LEDs of that type and the failure rate (probability of failing within one year). If an LED fails, what is the probability that it is type 1?
Table 3 |
||
Type |
Proportion of Total |
Failure Rate |
1 2 3 4 5 6 |
.30 .25 .20 .10 .05 .10 |
.0002 .0004 .0005 .0010 .0020 .0040 |
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