Weighted probability means :: For example, if you were rolling a single six-sided die, you would have the same probability of rolling a one as rolling any other number because each number will come up one out of six times

Now,

Probability of rolling a 1 = 1 * m ( let m be any multiplier)

similarly rolling 2 = 2* m

..

rolling 6 = 6 * m

These are the possible outcomes and since the probability must be 1

so add these possible outcomes : 1m + 2m + . . . + 6m = 1

or m = $\frac{1}{21}$

Now, as you have the multiplier

you can find all the probabilities

$1(\frac{1}{21}) + 2(\frac{1}{21}) + ... .. + 6(\frac{1}{21}) = \frac{13}{3}$

How is 1(1/21)+2(1/21)+.....+6(1/21)=13/3
Can you please explain? Isn't that 1??

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