Question

Non-equal probabilities Problem:
C​onsider non-symmetric dice for which probability to get kk points is proportional to kk, k=1,2,3,4,5,6k=1,2,3,4,5,6. (I.e. probability to get 2 is twice as large as probability to get 1.) What is the probability to get 1 point on this dice?

Answer 1

Given :   non-symmetric dice for which probability to get k  points is proportional to k , k=1,2,3,4,5,6  (I.e. probability to get 2 is twice as large as probability to get 1.

To Find :  the probability to get 1 point on this dice

Solution:

Probability to get 1  = x  

probability to get 2   = 2x

probability to get 3   = 3x

Probability to get 4  = 4x  

probability to get 5   = 5x

probability to get 6   = 6x

Total Probability = x + 2x + 3x + 4x + 5x + 6x  =   21x

probability to get 1 point on this dice  =  x/21x

= 1/21

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