assume the probability that an electronic device will have a type 1 defect is 1% and the probability that it will have a type 2 defect is 2%. given that these two defects are not independent ,what is the probability that an item randomly selected has both a type 1 and type 2 defect?
To calculate the probability that an item randomly selected has both a type 1 and type 2 defect, we need to know the relationship between these two defects. If they are independent, the probability can be calculated by multiplying the probabilities of each defect occurring separately. However, in this case, it is stated that these two defects are not independent.
Since we don't have additional information about the relationship between the defects, we cannot determine the exact probability. To proceed, we could consider the worst-case scenario, which is assuming that the occurrence of one defect increases the likelihood of the other.
In that case, we can assume that if an electronic device has a type 1 defect, it is more likely to have a type 2 defect. Let's say the probability of an item having a type 1 defect is 1% (0.01), and the probability of it having a type 2 defect given that it has a type 1 defect is 100% (1.00).
To calculate the probability of both defects occurring, we multiply these probabilities:
0.01 (probability of type 1 defect) * 1.00 (probability of type 2 defect given type 1 defect)
= 0.01
Therefore, the probability that an item randomly selected has both a type 1 and type 2 defect, assuming the worst-case scenario, is 0.01 or 1%.