The quality-control department of Starr Communications, the manufacturer of video-game cartridges, has determined from records that 1.7% of the cartridges sold have video defects, 0.9% have audio defects, and 0.2% have both audio and video defects.
a:What is the probability that a cartridge purchased by a customer will have a video or audio defect?
b: What is the probability that a cartridge purchased by a customer will not have a video or audio defect?
prob(video OR audio) = Prob(video) + prob(audio) - prob(video AND audio)
= .017 + .009 - .002
=
for b) just find 1 - (above prob)
To find the probability of a cartridge having a video or audio defect, we need to use the concept of "union" in probability theory. The probability of the union of two events is calculated by adding the probabilities of each individual event and then subtracting the probability of both events occurring together (to avoid double counting).
a: Probability of a video or audio defect:
The probability of a video defect is given as 1.7% or 0.017, and the probability of an audio defect is given as 0.9% or 0.009. However, we need to subtract the probability of both audio and video defects occurring together, which is given as 0.2% or 0.002. So, the probability of a cartridge having a video or audio defect is calculated as follows:
Video Defects probability = 0.017
Audio Defects probability = 0.009
Both Audio and Video Defects probability = 0.002
P(Video or Audio Defect) = P(Video Defect) + P(Audio Defect) - P(Both Audio and Video Defects)
= 0.017 + 0.009 - 0.002
= 0.024 (or 2.4%)
Therefore, the probability that a cartridge purchased by a customer will have a video or audio defect is 2.4%.
b: Probability of no video or audio defect:
To find the probability that a cartridge will not have a video or audio defect, we need to subtract the probability of a video or audio defect from 1 (since the sum of all possible outcomes should equal 1).
P(No Video or Audio Defect) = 1 - P(Video or Audio Defect)
= 1 - 0.024
= 0.976 (or 97.6%)
Therefore, the probability that a cartridge purchased by a customer will not have a video or audio defect is 97.6%.