Answer:
(a) The probability that a selected joint was judged to be defective by neither of the two inspectors is 0.906.
(b) The probability that a selected joint was judged to be defective by inspector B but not by inspector A is 0.0213.
Step-by-step explanation:
The sample of joints randomly selected is, <em>n</em> = 10,000.
Number of joints judged defective by inspector <em>A</em> is, <em>n</em> (A) = 727.
The probability that a joint is judged defective by inspector <em>A</em> is:
Number of joints judged defective by inspector <em>B </em>is, <em>n</em> (B) = 756.
The probability that a joint is judged defective by inspector <em>B</em> is:
Number of joints judged defective by at least one of the inspectors is,
<em>n</em> (At least 1) = 940.
The probability that a joint is judged defective by at least one of the inspectors is:
(a)
Compute the probability that a selected joint was judged to be defective by neither of the two inspectors as follows:
P (At least 1) = 1 - P (Less than 1)
= 1 - P (None)
P (None) = 1 - P (At least 1)
Thus, the probability that a selected joint was judged to be defective by neither of the two inspectors is 0.906.
(b)
Compute the probability that a selected joint was judged to be defective by inspector B but not by inspector A as follows:
P (B but not A) = P (At least 1) - P (A)
Thus, the probability that a selected joint was judged to be defective by inspector B but not by inspector A is 0.0213.