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  • The probability of a number n showing in a throw of a dice marked 1 to 6 is proportional to n. Then the probability of the number 3 showing in a throw isOpt

The probability of a number n showing in a throw of a dice marked 1 to 6 is proportional to n. Then the probability of the number 3 showing in a throw is

Option: 1

\frac{1}{2}


Option: 2

\frac{1}{6}


Option: 3

\frac{1}{7}


Option: 4

\frac{1}{21}


Answers (1)

best_answer

\begin{aligned} & \mathrm{P\left(E_n\right)=\text { probability of the dice showing } n=k n} . \\ \\& \text { Clearly, } \mathrm{P\left(E_1\right)+P\left(E_2\right)+\ldots+P\left(E_6\right)=1} \\ \\& \mathrm{\therefore \quad k(1+2+3+4+5+6)=1} \\ \\& \mathrm{\therefore \quad k=\frac{1}{\frac{6 \cdot 7}{2}}=\frac{1}{21} \cdot \text { So, } P\left(E_3\right)=k \cdot 3=\frac{1}{21} \times 3=\frac{1}{7} .} \end{aligned}

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Nehul

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