The probability of a sample that contains exactly two defective parts is 13.1926.
As we know if P is the probability of achieving k results in n trials then the probability formula is P = [tex]({}^{n}_{k})[/tex][tex]p^{k}[/tex][tex]q^{n-k}[/tex]
In this formula n = number of trials
k = number of success
(n-k) = number of failures
p = probability of success in one trial
q = (1-p) = probability of failure in one trial
In this sum n = 10
k = 3
number failures (n-k) = (10 - 3) = 7
p = 3% which can be written as 0.03
q = 97% Which can be written as 0.97
Now putting these values in the formula
P = [tex]({}^{10}_{3})[/tex][tex]0.03^{3}[/tex][tex]0.97^{10-3}[/tex]
P = [tex]({}^{10}_{3})[/tex][tex]0.03^{3}[/tex][tex]0.97^{7}[/tex]
P = (10! ÷ 3!) × 0.000027 × 0.8079
P = 13.1926
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