In a production run of 300 units there are exactly 20 defect

In a production run of 300 units, there are exactly 20 defective items and 280 good items.

a) What is the probability that a randomly selected item is defective?

b) If two items are sampled without replacement, what is the probability that both are good?

c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?

Solution

a)The probability that a randomly selected item is defective is: 20/300=0.06

b)If two items are sampled without replacement, then the probability that both are good is: 280*279/(300*299)=0.868

c)If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective:280/300*20/299=0.06