Question

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 15 wood and 14 graphite are defective and one racket is randomly selected from the​ sample, find the probability that the racket is wood or defective.

Answer 1

The probability that the racket is wood or defective is 0.57.

Explanation:

Let W represents wood racket, G represents the graphite racket and D represents the defective racket,

Given,

n(W) = 100,

n(G) = 100,

⇒ Total rackets = 100 + 100 = 200

n(W∩D) = 15,

n(G∩D) = 14,

⇒ n(D) = n(W∩D) + n(G∩D) = 15 + 14 = 29,

We know that,

n(W∪D) = n(W) + n(D) - n(W∩D)

= 100 + 29 - 15

= 100 + 14

= 114,

Hence, the probability that the racket is wood or defective,

`P(W\cup D) = (114)/(200)`

`=0.57`