Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{6}$
• C. $\frac{1}{7}$
• D. $\frac{1}{21}$

Answer 1

The correct option is C $\frac{1}{7}$

$P\left(k\right)$ = Probability of showing no. $k$= $Ck$
also
$P\left(1\right)+P\left(2\right)+..+P\left(6\right)=1$
$C+2C+..6C=1$
$6(6+1)C/2=1$
$C=\frac{1}{21}$
$P\left(3\right)=3C=1/7$