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?
+33614 "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.
