Question

The quality-control department of Starr Communications, the manufacturer of video-game cartridges, has determined from records that 1.6% of the cartridges sold have video defects, 0.7% have audio defects, and 0.4% 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?

Answer 1

The probability that a cartridge purchased by a customer will have a video or audio defect is 1.9%

Explanation:

The given parameters in the question are;

The percentage of cartridges that have video defects, P(X) = 1.6%

The percentage of cartridges that have audio defects, P(Y) = 0.7%

The percentage of cartridges that have both audio and video defects, P(X and Y) = 0.4%

The probability is with regards to inclusive evets

The probability of inclusive events 'X' and 'Y' which are events that can happen at the same time are given as follows;

P(X or Y) = P(X) + P(Y) - P(X and Y)

Therefore, we have;

P(X or Y) = P(Video or Audio) = 0.016 + 0.007 - 0.004 = 0.019

∴ P(Video or Audio) = 1.9%

The probability that a cartridge purchased by a customer will have a video or audio defect = 1.9%