A machine produces batches of 10 light-bulbs at a time. The probability any given light bulb will be defective is 15%. A batch is rejected if at least 3 light-bulbs are defective. Find the probability a given batch is rejected.

Name: A machine produces batches of 10 light-bulbs at a time. The probability any given light bulb will be defective is 15%. A batch is rejected if at least 3 light-bulbs are defective. Find the probability a given batch is rejected.
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1 - \left( \left( \begin{array} { c } 10 \0\end{array} ight) ( .85 ) ^ { 10 } ( .15 ) ^ { 0 } + \left( \begin{array} { c } 10 \1\end{array} ight) ( .85 ) ^ { 9 } ( .15 ) ^ { 1 } + \left( \begin{array} { c } 10 \2\end{array} ight) ( .85 ) ^ { 8 } ( .15 ) ^ { 2 } ight) = .18

A Machine Produces Batches of 10 Light-Bulbs at a Time