Question

Question 7
Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by 10 feet contains no flaws?

Answer 1

Answer on Question #43780 – Math – Statistics and Probability

Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by 10 feet contains no flaws?

Solution:

The area of a carpet is $8*10=80$. Notice that $X \sim Poisson\left(\frac{80}{200} = \frac{2}{5} = 0.4\right)$. Then the probability that the carpet contains no flaws is $P(X = 0) = \frac{0.4^0 e^{-0.4}}{0!} = 0.67$.

Answer. 0.67

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