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A die is loaded such that the probability of throwing the number \(i\) is proportional to its reciprocal. The probability that 3 appears in a single throw is-
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\(\begin{aligned}
& \mathrm{P}(\mathrm{i})=\frac{\mathrm{k}}{\mathrm{i}} \Rightarrow \mathrm{1}=\sum_{\mathrm{i}=1}^6 \mathrm{P}(\mathrm{i})=\mathrm{k} \sum_{\mathrm{i}=1}^6 \frac{1}{\mathrm{i}}=\mathrm{k} \frac{49}{20} \\
& \Rightarrow \mathrm{k}=\frac{20}{49} . \mathrm{P}(3)=\frac{20}{147}
\end{aligned}\)
& \mathrm{P}(\mathrm{i})=\frac{\mathrm{k}}{\mathrm{i}} \Rightarrow \mathrm{1}=\sum_{\mathrm{i}=1}^6 \mathrm{P}(\mathrm{i})=\mathrm{k} \sum_{\mathrm{i}=1}^6 \frac{1}{\mathrm{i}}=\mathrm{k} \frac{49}{20} \\
& \Rightarrow \mathrm{k}=\frac{20}{49} . \mathrm{P}(3)=\frac{20}{147}
\end{aligned}\)
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