Question

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 6 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

Answer: Probability that the racket is wood or defective is 0.57.

Step-by-step explanation:

Since we have given that

Number of wood tennis rackets = 100

Number of graphite tennis rackets = 100

Total rackets = 100+100 = 200

Number of defected wood tennis rackets = 6

Number of defected graphite tennis rackets = 14

Total defective = 6+14 = 20

We need to find the probability that the racket is wood or defective.

So, Probability that the racket is wood or defective is given by

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

Let A be the event for wood.

Let B be the event for defective.

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=\dfrac{100}{200}+\dfrac{20}{200}-\dfrac{6}{200}\\\\P(A\cup B)=\dfrac{100+20-6}{200}\\\\P(A\cup B)=\dfrac{114}{200}\\\\P(A\cup B)=0.57$

Hence, Probability that the racket is wood or defective is 0.57.

Answer 2

The probability that the racket  is wood or defective is 0.57

Further explanation

Probability is a measure quantifying the likelihood that events will occur. Probability quantifies as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability also means the number of ways of achieving success, the total number of possible outcomes.

There are 3 basic rules associated with probability: the addition, multiplication, and complement rules.

The addition rule is used to calculate the probability of event A or event B happening, we express it as: $P(A or B) = P(A) + P(B) - P(A and B)$

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 6 wood and 14  graphite are defective and one racket is randomly selected from the sample

Total $100w+100g=200$

Defective $6w+14g= 20$

$\frac{100}{200} + \frac{14}{200 }  =\frac{114}{200}$

$\frac{100}{200} + \frac{14}{200 }  = 0.57$

Remove the ones that are wood and defective, then The probability that the racket  is wood or defective is  0.57

• a. 0.525
• b. 0.57
• c. 0.075
• d. There is insufficient information to answer the question

Learn more

1. Learn more about the probability https://brainly.com/question/7965468
2. Learn more about randomly selected https://brainly.com/question/3552442
3. Learn more about  the probability of sample https://brainly.com/question/5975944

Answer details

Grade:  9

Subject:  mathematics

Chapter:  probability

Keywords: the probability, randomly selected, the racket, wood, defective