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A box contain 12 items out of which 4 are defective. A persons selects 6 items from the box. The expected number of defective items out of his selected items is: (a) 2 (b) 3 (c) \( 3 / 2 \) (d) none of the above |
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Answer» Correct option is (d) none of the above \(p = \frac4{12}= \frac13\) \(q = 1 - p = 1 - \frac13 = \frac23\) \(n= 6\) \(P(X =r) =\, ^nC_r \,p^r\,q^{n -r}\) \(= \,^6C_r\,p^r\,q^{6-r}\) \((\because n = 6)\)
\(E(X) = \displaystyle\sum^4_{i = 0} x_i(P(x_i))\) \(= 0.\left(\frac23\right)^6 + 1. 2\left(\frac23\right)^5 + 2. \left(\frac53\right)\left(\frac23\right)^4+ 3.\left(\frac{20}{27}\right)\left(\frac23\right)^3 + 4 . \frac5{27}.\left(\frac23\right)^2\) \(= \frac{64}{243}+ \frac{160}{243}+ \frac{160}{243}+\frac{80}{243}\) \(= \frac{464}{243}\) \(= 1.9\) |
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