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 independent events, then the probability that they happen together is just the product of their probabilities.

Thus,

P(X and y are warped) = P(X is warped) P(Y is warped)

= 0.05*0.02

= 0.001 or 0.1% [answer]