Question

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. if 13 wood and 10 graphite are defective and one racket is randomly selected from the​ sample, find the probability that the racket is wood or defective.

Answer 1

Let's split the problem in non-intersecting subsets: we have $87$ good wood racquets, $13$ defective wood rackets, $90$ good graphite racquets, $10$ defective graphite rackets.

The probability that the racket is wood or defective covers the following subsets: good wood, defective wood and defective graphite, which have, respectively, $87$, $13$ and $10$ elements.

Since the total is $200$ elements, the probability is

$\frac{87+13+10}{200} = \frac{110}{200} = 0.55$