Question

A box contains 20 DVDs, 4 of which are defective If two DVDs are selected at random (with replacement) from this box, what is the probability that both are defective?

Answer 1

The probability of selecting two defective DVDs from a box containing 20 DVDs with 4 defective ones, with replacement, is 1/25.

Step-by-step explanation:

To find the probability that both DVDs are defective, we need to consider the probability of selecting a defective DVD on each trial.

Since the DVDs are selected with replacement, the probability remains constant.

There are 20 DVDs in total, with 4 of them being defective.

So the probability of selecting a defective DVD on the first trial is 4/20 = 1/5.

Similarly, the probability of selecting a defective DVD on the second trial is also 1/5.

To find the probability that both DVDs are defective, we multiply these probabilities together:

Probability = (1/5) * (1/5) = 1/25

Answer 2

1/25

Step-by-step explanation:

Total number of DVD's in the box = 20

Number of defective DVD's = 4

The probability of picking up a defective DVD =
`(4)/(20)=(1)/(5)`

This DVD is being replaced back. So this does not change the total number of DVD's in the box and the number of defective DVD's in the box.

So again the probability of picking up the second defective DVD =
`(4)/(20)=(1)/(5)`

The probability that both DVD's are defective will be the product of probabilities of individual events i.e.

`(1)/(5) * (1)/(5)  = (1)/(25)`

Thus, the probability that both DVDs are defective is 1/25