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Probability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSProbability3 Marks
Question
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
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Answer

S = {(1, 2), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (1, 3), (2, 3), (3, 2), (4, 2), (5, 2), (6, 2), (1, 4), (2, 4), (3, 4), (4, 3), (5, 3), (6, 3), (1, 5), (2, 5), (3, 5), (4, 5), (5, 4), (6, 4), (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6)} n(S) = 30 Let X denotes the larger of the two numbers obtained.
$\text{x}_i$ $\text{f}_i$ $\text{p}_i$ $\text{p}_i\text{x}_i$
$2$
$3$
$4$
$5$
$6$		 $2$
$4$
$6$
$8$
$10$		 $\frac{2}{30}$
$\frac{4}{30}$
$\frac{6}{30}$
$\frac{8}{30}$
$\frac{10}{30}$		 $\frac{4}{30}$
$\frac{12}{30}$
$\frac{24}{30}$
$\frac{40}{30}$
$\frac{60}{30}$
  $30$   $\sum\text{p}_i\text{x}_i=\frac{140}{30}$
$\text{E}(\text{X})=\sum\text{p}_i\text{x}_i=\frac{140}{30}=\frac{14}{3}=4\frac{2}{3}$

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