Probabilities are used to determine the chances of events
- The probability with replacement is 0.7742, while the probability without replacement is 0.7741
- The probability with replacement is independent, while the probability without replacement is dependent
From the table (see attachment), we have:
[tex]\mathbf{Order\ Accurate = 331 + 269 + 245 +144}[/tex]
[tex]\mathbf{Order\ Accurate = 989}[/tex]
[tex]\mathbf{Order\ Not\ Accurate = 34 + 53 + 30 + 18}[/tex]
[tex]\mathbf{Order\ Not\ Accurate = 135}[/tex]
(a) Probability that both orders are accurate (with replacement)
This is calculated using:
[tex]\mathbf{Pr = \frac{Order\ Accurate}{Total} \times \frac{Order\ Accurate}{Total}}[/tex]
So, we have:
[tex]\mathbf{Pr = \frac{989}{989+135} \times \frac{989}{989 + 135}}[/tex]
[tex]\mathbf{Pr = \frac{989}{1124} \times \frac{989}{1124}}[/tex]
[tex]\mathbf{Pr = 0.7742}[/tex]
The events are independent, because the first selection does not affect the second
(b) Probability that both orders are accurate (without replacement)
This is calculated using:
[tex]\mathbf{Pr = \frac{Order\ Accurate}{Total} \times \frac{Order\ Accurate - 1}{Total - 1}}[/tex]
So, we have:
[tex]\mathbf{Pr = \frac{989}{989+135} \times \frac{989 - 1}{989 + 135 - 1}}[/tex]
[tex]\mathbf{Pr = \frac{989}{1124} \times \frac{988}{1123}}[/tex]
[tex]\mathbf{Pr = 0.7741}[/tex]
The events are dependent, because the first selection affects the second
Read more about probabilities at:
https://brainly.com/question/11234923
