Statistics

A sample of 4 different calculators is randomly selected from a group containing

20 that are defective and

37 that have no defects.

Find the probability that at least one of the calculators is defective. Round to the nearest thousandth.

$\begin{array}{|rcll|} \hline && \frac{ \binom{20}{1} \cdot \binom{37}{3} } {\binom{57}{4} } \\ &=& \frac{ 20 \cdot \frac{37}{3} \cdot \frac{36}{2} \cdot \frac{35}{1} } { \frac{57}{4} \cdot \frac{56}{3} \cdot \frac{55}{2} \cdot \frac{54}{1} } \\ &=& 4\cdot \frac{ 20 \cdot 37 \cdot 36 \cdot 35 } { 57 \cdot 56 \cdot 55 \cdot 54 } \\ &=& 0.39340776183 \\ &\approx& 0.393\quad (39.3\ \% ) \\ \hline \end{array}$