A purse contains four coins each of which is either a rupee or two rupees coin. Find the expected value of a coin in that purse.

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Solution

Various possibilities of coins in the purse can be

$p_{i}$
$M_{i}$
$p_{i} M_{i}$
(i) 4 1 rupee coins
$\frac{1}{16}$
4
$\frac{4}{16}$
(ii) 3 one Rs.+1 two Rs.
$\frac{4}{16}$
5
$\frac{20}{16}$
(iii) 2 one Rs.+2 two Rs.
$\frac{6}{16}$
6
$\frac{36}{16}$
(iv) 1 one Rs.+3 two Rs.
$\frac{4}{16}$
7
$\frac{28}{16}$
(iv) 4 two Rs.
$\frac{1}{16}$
8
$\frac{8}{16}$

6 / -
Hence expected value is Rs, $6 / -$

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	$p_{i}$	$M_{i}$	$p_{i} M_{i}$
(i) 4 1 rupee coins	$\frac{1}{16}$	4	$\frac{4}{16}$
(ii) 3 one Rs.+1 two Rs.	$\frac{4}{16}$	5	$\frac{20}{16}$
(iii) 2 one Rs.+2 two Rs.	$\frac{6}{16}$	6	$\frac{36}{16}$
(iv) 1 one Rs.+3 two Rs.	$\frac{4}{16}$	7	$\frac{28}{16}$
(iv) 4 two Rs.	$\frac{1}{16}$	8	$\frac{8}{16}$
			6 / -

A purse contains four coins each of which is either a rupee or two rupees coin. Find the expected value of a coin in that purse.

Various possibilities of coins in the purse can bepiMipiMi(i) 4 1 rupee coins1164416(ii) 3 one Rs.+1 two Rs.41652016(iii) 2 one Rs.+2 two Rs.61663616(iv) 1 one Rs.+3 two Rs.41672816(iv) 4 two Rs.11688166 / -Hence expected value is Rs, 6/−