Two different record companies X and Y both produce classica

Two different record companies, X and Y, both produce classical music recordings. Label X is a “budget” label, and 5% of X’s new records exhibit a significant degree of warpage. Label Y is manufactured under more stringent quality control conditions (and hence sold at a higher price) than X, so only 2% of its new pressings are warped. If you purchase one label X record and one label Y record from a record seller, what is the probability that both records are warped?

Solution

As they are independently warped, then for them to happen together, we multiply their probabilities:

P(both are warped) = P(x warped) P(y warped) = 0.05*0.02 = 0.001 or 0.1% [ANSWER]