7 fair 6-sided dice are tossed. What is the probability of getting a total of either one of two primes:31 or 37? Thanks for any help.
In problems of this type, we just use the coefficients of n^31 and n^37 in the expansion of this polynomial: expand [n+n^2+n^3+n^4+n^5+n^6]^7:
The coefficient of n^31 =9,142, which are the odds out of 6^7, or =9,142/6^7 =0.032657.
The coefficient of n^37 =462, which are the odds out of 6^7, or 462 / 6^7 =0.00165037.
Therefore, the probability of getting either a total of 31 or a 37 is=0.032657+0.00165037=~3.43%
