There are two urns, each with some numbered cards inside.
In urn A there are cards representing all 3-digit numbers (from 109 to 910 inclusively), having 10 as their sum of digits.
In urn B - all 3-digit numbers (from 119 to 920 inclusively), with 11 as their s.o.d.

Assuming you aim to randomly draw a prime number, which urn would you choose?
What if there was a 3rd urn with s.o.d=15, would you consider it as a good choice?

    5   Digsum=10
   10      for N=100 to 999
   20      S=fnSod(N)
   30        if S=Digsum and prmdiv(N)=N then print N;:inc Ct:next
   35        if S=Digsum then inc Ct2:next
   40      next
   50      print:print Ct,Ct2,Ct/Ct2
   60      end
 1070     fnSOD(X)
 1080        Sod=0
 1090        S=cutspc(str(X))
 1100        for I=1 to len(S)
 1110          Sod=Sod+val(mid(S,I,1))
 1120        next
 1130      return(Sod)

finds the primes
 109  127  163  181  271  307  433  523  541  613  631  811
 
which are 12  out of the 42 cards for prob = 0.2857142857142857142

Changing the digital sum to 11 gives

 137  173  191  227  263  281  317  353  443  461  641  821  911
or 13 out of 48, with prob = 0.2708333333333333333

so the former urn is better.

When the s.o.d. is 15 all numbers are multiples of three and therefore have no primes. That urn would not be a good choice.

Posted by Charlie on 2013-01-10 18:36:33