A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 6 wood and 14

Mathematics

2 answers:

Vlad1618 [11]3 years ago

7 0

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.

STALIN [3.7K]3 years ago

7 0

The probability that the racket is wood or defective is 0.57

<h3>Further explanation </h3>

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 $100w+100g=200$