What is the probability of rolling "$1$" on a die for which the probability of rolling "$k$" is proportional to $k$, for $k=1,2,3,4,5,6$?

Question

I am new to mathematics for data science can any one solve my question?

C​onsider a non-symmetric die for which probability to get $k$ points is proportional to $k$, for $k=1,2,3,4,5,6$. (I.e., the probability to get "$2$" is twice as large as the probability to get "$1$".)

What is the probability to get $1$ point on this die?

Answer 1

First, understand the probability. The ratio of the probability of getting $1, 2, 3, 4, 5, $ and $6$ respectfully is $1:2:3:4:5:6$. Adding the ratios gets us $21$, and getting a $1$ on the dice equals $\frac{1}{21}$ (since we have that $1$ corresponds to $1$.)

Therefore, the answer is $$\boxed{\frac{1}{21}}.$$

-FruDe