Answer: Option D
[tex]P=0.3079[/tex]
Step-by-step explanation:
We can use the binomial formula to solve this problem.
[tex]P(X=x)=\frac{n!}{x!(n-x)!}*p^x(1-p)^{n-x}[/tex]
Where p is the probability of success, n is the sample size and x is the number of successes expected.
Note that in this case
[tex]p = 0.02[/tex] (probability that a part is defective)
[tex]n = 25[/tex]
[tex]x = 1[/tex]
Then we calculate the probability
[tex]P(X=1)=\frac{25!}{1!(25-1)!}*0.02^x(1-0.98)^{25-1}[/tex]
[tex]P(1)=0.3079[/tex]
