Answer:
a
The probability that the selected joint was judged to be defective by neither of the two inspectors is [tex]P(A' n B' ) = 0.8855[/tex]
b
The probability that the selected joint was judged to be defective by inspector B but not by inspector A is [tex]P(A' n B) =0.0403[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_s = 10000[/tex]
The number of outcome for inspector A is [tex]n__{A}} = 742[/tex]
The number of outcome for inspector B is [tex]n__{B}} = 745[/tex]
The number of joints judged defective by both inspector is [tex]n(A u B) = 1145[/tex]
The the probability that the selected joint was judged to be defective by neither of the two inspectors is mathematically represented as
[tex]P(A' n B' ) = 1 - P(A u B)[/tex]
Now
[tex]P(A\ u \ B) = \frac{n(Au B)}{n_s }[/tex]
substituting values
[tex]P(A\ u \ B) = \frac{1145}{ 10 000 }[/tex]
So
[tex]P(A' n B' ) = 1 - \frac{1145}{10 000}[/tex]
[tex]P(A' n B' ) = 0.8855[/tex]
the probability that the selected joint was judged to be defective by inspector B but not by inspector A is mathematically represented as
[tex]P(A' n B) = P(A \ u \ B) -P(A)[/tex]
Now
[tex]P(A) = \frac{n__{A}}{n_s}[/tex]
substituting values
[tex]P(A) = \frac{742}{10 000}[/tex]
So
[tex]P(A' n B) = \frac{1145}{10 000} - \frac{742}{10 000}[/tex]
[tex]P(A' n B) =0.0403[/tex]
