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Probability — Maths STD 12 Science — Question

Gujarat 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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