In a game, the probabilities of winning an amount(x) are given in the table below. The expected payout is the weighted mean of the observations with their probabilities. Find the expected payout.
$\begin{matrix} A m o u n t (x) & 0 & 10 & 20 & 30 & 40 & 50 & 60 P r o b a b i l i t y (w) & 0.25 & 0.2 & 0.15 & 0.15 & 0.1 & 0.1 & 0.05 \end{matrix}$

Rs. 18

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Rs. 21.5

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Rs. 24.5

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Rs. 30

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Solution

The correct option is B Rs. 21.5
$W e i g h t e d m e a n = \frac{\sum W X}{\sum W} \sum W X = 0.25 \times 0 + 0.2 \times 10 + 0.15 \times 20 + 0.15 \times 30 + 0.1 \times 40 + 0.1 \times 50 + 0.05 \times 60 = 0 + 2 + 3 + 4.5 + 4 + 5 + 3 = 21.5 \sum W = 0.25 + 0.2 + 0.15 + 0.15 + 0.1 + 0.1 + 0.05 = 1 E x p e c t e d P a y o u t = \frac{21.5}{1} = R s . 21.5$

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In a game, the probabilities of winning an amount(x) are given in the table below. The expected payout is the weighted mean of the observations with their probabilities. Find the expected payout. Amount (x)0102030405060Probability (w)0.250.20.150.150.10.10.05

The correct option is B Rs. 21.5Weighted mean=∑WX∑W∑WX=0.25×0+0.2×10+0.15×20+0.15×30+0.1×40+0.1×50+0.05×60=0+2+3+4.5+4+5+3=21.5∑W=0.25+0.2+0.15+0.15+0.1+0.1+0.05=1Expected Payout=21.51=Rs. 21.5