A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 88 wood and 1111 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

The question is wrong since it is not possible to have 111 defective graphite rackets when the total number of graphite racket is 100.

Question:

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. Assuming that If 88 wood and 90 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

Given Information:

Total wood = 100

Total graphite = 100

Defective wood = 88

Non-defective wood = 12

Defective graphite = 90

Non-defective graphite = 10

Required Information:

Probability of racket being selected is wood or defective = ?

Answer:

P (wood or defective) = 0.95

Step-by-step explanation:

The probability of selecting a wood racket is

P (wood) = number of wood rackets/total number of rackets

P (wood) = 100/200 = 1/2

The probability of selecting a defective racket is

P (defective) = number of defective rackets/total number of rackets

P (defective) = 88+90/200 = 178/200 = 89/100

There is double counting of wood so we have to subtract the probability of wood and defective

P (wood and defective) = 88/200 = 11/25

P (wood or defective) = P (wood) + P (defective) - P (wood and defective)

P (wood or defective) = 1/2 + 89/100 - 11/25

P (wood or defective) = 0.95

Alternatively:

P (defective) = number of defective rackets/total number of rackets

P (defective) = 88+90/200 = 178/200 = 89/100

P (wood and non-defective) = 12/200 = 3/50

There is no double counting here so we dont have to subtract anything

P (wood or defective) = P (wood) + P (wood and non-defective)

P (wood or defective) = 89/100 + 3/50

P (wood or defective) = 0.95