Final answer:
The probability that out of a sample of 5 pens drawn one by one with replacement, at most one is defective is 0.824.
Step-by-step explanation:
To find the probability that at most one pen is defective out of a sample of 5 pens drawn one by one with replacement, we need to consider two cases: when there are no defective pens and when there is one defective pen.
For the first case, the probability is (30/50) * (29/49) * (28/48) * (27/47) * (26/46) because we are drawing 5 non-defective pens.
For the second case, the probability is (20/50) * (30/49) * (29/48) * (28/47) * (27/46) because we are drawing 1 defective pen and 4 non-defective pens.
The total probability is the sum of these two cases: (30/50) * (29/49) * (28/48) * (27/47) * (26/46) + (20/50) * (30/49) * (29/48) * (28/47) * (27/46) = 0.824.