Question

The quality-control department of Starr Communications, a manufacturer of video-game DVDs, has determined from records that 1.5% of DVDs sold have video defects, 0.8% have audio defects, and 0.4% have both audio and video defects. What is the probability that a DVD purchased by a customer a. will have a video or audio defect? b. Will not have a video or audio defect?

Answer 1

Let A represents the event that DVD has a video effect.
So,
P(A) = 1.5 %

Let B represents the event that DVD has a audio defect.
So,
P(B) = 0.8 %

A ∩ B represents that DVD has both audio and video defect.
So,
P(A∩B) = 0.4%

Part a)
A ∪ B represents that DVD has a video or audio defect.

P(A∪B) = P(A)+P(B)-P(A∩B) = 1.5 + 0.8 - 0.4 = 1.9%

Thus the probability that the DVD purchased by the customer has a video or audio defect is 1.9%.

Part b)
The complement of P(A∩B) will represent the probability that the DVD does not have video or audio defect.

So, the probability that DVD purchased by customer does not have video or audio defect is 1 - 0.4 = 0.96%