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?

Accepted Solution

Answer:1/25Step-by-step explanation:Total number of DVD's in the box = 20Number of defective DVD's = 4The probability of picking up a defective DVD = [tex]\frac{4}{20}=\frac{1}{5}[/tex]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 = [tex]\frac{4}{20}=\frac{1}{5}[/tex]The probability that both DVD's are defective will be the product of probabilities of individual events i.e.[tex]\frac{1}{5} \times \frac{1}{5} Β = \frac{1}{25}[/tex]Thus, the probability that both DVDs are defective is 1/25