Let's split the problem in non-intersecting subsets: we have [tex] 87 [/tex] good wood racquets, [tex] 13 [/tex] defective wood rackets, [tex] 90 [/tex] good graphite racquets, [tex] 10 [/tex] 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, [tex] 87 [/tex], [tex] 13 [/tex] and [tex] 10 [/tex] elements.
Since the total is [tex] 200 [/tex] elements, the probability is
[tex] \frac{87+13+10}{200} = \frac{110}{200} = 0.55 [/tex]
