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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.

Guest Mar 6, 2017
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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.

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

heureka  Mar 6, 2017