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 Two urns (Posted on 2013-01-10)
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?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer assisted solution | Comment 1 of 5

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

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