A manufacturing machine has a 4% defect rate.
If 3 items are chosen at random, what is the probability that at least one will have a defect?
To find the probability that at least one item will have a defect, we need to find the complement of the probability that none of the items will have a defect.
The probability of an item not having a defect is 1 minus the defect rate, which is 1 - 0.04 = 0.96.
To find the probability that none of the three items will have a defect, we multiply the probabilities together since each item is chosen independently.
Probability of none of the items having a defect = (0.96) * (0.96) * (0.96) = 0.88473 (rounded to 5 decimal places).
The probability of at least one item having a defect is the complement of the probability of none of the items having a defect.
Probability of at least one item having a defect = 1 - 0.88473 = 0.11527 (rounded to 5 decimal places).
Therefore, the probability that at least one item will have a defect is approximately 0.11527 or 11.527%.
To find the probability that at least one item will have a defect, we need to calculate the probability that all three items will not have a defect and subtract it from 1.
The probability that a single item will not have a defect is 1 minus the defect rate, which is 1 - 0.04 = 0.96.
To find the probability that all three items will not have a defect, we multiply the probabilities of each item not having a defect together. So, the probability is:
P(all three items not having a defect) = 0.96 * 0.96 * 0.96 = 0.884736.
Finally, to find the probability that at least one item will have a defect, we subtract the probability of none of the items having a defect from 1:
P(at least one item having a defect) = 1 - P(all three items not having a defect) = 1 - 0.884736 = 0.115264.
Therefore, the probability that at least one item will have a defect is approximately 0.1153, or 11.53%.