the solve of the shipment of 10 items has 2 items defective and 8 items are non defective.IN THE inspection of the shipment a sample of items will be selected and tested.if a defective items is found the shipment of 10 items will rejected.in a sample of 5 items what is the probability that the shipment will be rejected??
To find the probability that the shipment will be rejected, we need to calculate the probability of selecting a defective item in the sample of five items.
Let's determine the probability of selecting a defective item first. Out of the ten items in the shipment, two are defective and eight are non-defective. Therefore, the probability of selecting a defective item from the shipment is 2/10, or 1/5.
Now, since we are selecting a sample of five items, we have to consider different scenarios in which a defective item can be chosen. The defective item can be at any position within the sample. So, the probability of choosing one defective item out of five is:
P(choosing 1 defective item) = P(defective at position 1) + P(defective at position 2) + P(defective at position 3) + P(defective at position 4) + P(defective at position 5)
Since the probability of choosing a defective item is the same for each position, we can write:
P(choosing 1 defective item) = 5 * (1/5 * 4/9 * 5/8 * 6/7 * 7/6) [Each term represents the probability of selecting a defective item at its respective position]
Simplifying this equation:
P(choosing 1 defective item) = 5 * (4/9 * 5/8 * 7/6)
= 140/432
= 35/108
Therefore, the probability of the shipment being rejected (i.e., at least one defective item being found in the sample) is 35/108.