Question

A batch of 500 containers of frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement, from the batch. Let A and B denote the events that the fi rst and second containers selected are defective, respectively. (a) Are A and B independent events? (b) If the sampling were done with replacement, would A and B be independent?

Answer 1

(a) No, A and B are independent events.

(b) Yes, A and B be independent events if the sampling were done with replacement.

Explanation:

We are given that a batch of 500 containers of frozen orange juice contains 5 that are defective.

From this two containers are selected without replacement from the batch.

Where A and B denote the events that the first and second containers selected are defective, respectively.

(a) No, in this case A and B are not independent events because after selecting first defective container, the chances for selecting second defective container is affected as then the remaining defective containers will be 4 as we have not replaced the first one selected into the batch.

Hence, A and b events are not independent events.\

(b) If the sampling were done with replacement, then Yes A and B are independents events because with replacement means that selecting of one outcome does not affect the the selection chances for another events as after selecting first defective container and replacing it into the batch and then further selected another defective container will have the same probability.