1. 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

2. The enrollment in a certain course is 10% first-year students, 30% sophomores, 40% juniors, and 20% seniors. Experience has shown that the likelihood of receiving an A in the course is .2 for first-year students, .4 for sophomores, .3 for juniors, and .1 for seniors. Find the probability that a student who receives an A is a sophomore.
Use Bayes' theorem to calculate the probabilities?

Transcribed Image Text:

Proportion of Total Type Failure Rate 30 .0002 25 .0004 3 20 .0005 .10 4 .0010 .05 .0020 6. 10 .0040