Answer to Question #317043 in Statistics and Probability for Kiddo

Question

A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 9 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.

Answer 1

$X-number\,\,of\,\,defective\,\,fuses, X\sim Bin\left( 9,1-0.954 \right) =Bin\left( 9,0.046 \right) \\P\left( X\geqslant 3 \right) =1-P\left( X=0 \right) -P\left( X=1 \right) -P\left( X=2 \right) =\\=1-C_{9}^{0}\cdot 0.046^0\cdot 0.954^9-C_{9}^{1}\cdot 0.046^1\cdot 0.954^8-C_{9}^{2}\cdot 0.046^2\cdot 0.954^7=0.00663173$