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For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of 7 on the two dice?

 Mar 10, 2020
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"For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of 7 on the two dice?"

 

pn = n/21,  n = 1,2,3,4,5,6   so that the sum of the probabilities is unity (pn is probability a single die shows n).

 

To get 7 we must have 

1 and 6  or 6 and 1    p1+6 = 2*(1/21)*(6/21)

2 and 5 or 5 and 2     p2+5 = 2*(2/21)*(5/21)

3 and 4 or 4 and 3     p3+4 = 2*(3/21)*(4/21)

 

Overall probability = p1+6 + p2+5 +p3+4 

 

I'll leave you to do the number crunching.

 Mar 10, 2020
edited by Alan  Mar 10, 2020

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