Three dice

The player throwing the three dice asked G. Galilei the question: "Should I bet on the sum of 11 or the sum of 12?" What did Galilei answer him?

Hint: write down all three triples of numbers that can be thrown and:
have a total of 11
have a total of 12

and compare probabilities.

Correct answer:

p11 =  0.125
p12 =  0.1157
v =  11

Step-by-step explanation:

n=6 6 6=216 s1=1+4+6=11 s2=1+5+5=11 s3=1+6+4=11 s4=2+3+6=11 s5=2+4+5=11 s6=2+5+4=11 s7=2+6+3=11 s8=3+2+6=11 s9=3+3+5=11 s10=3+4+4=11 s11=3+5+3=11 s12=3+6+2=11 s13=4+1+6=11 s14=4+2+5=11 s15=4+3+4=11 s16=4+4+3=11 s17=4+5+2=11 s18=4+6+1=11 s19=5+1+5=11 s20=5+2+4=11 s21=5+3+3=11 s22=5+4+2=11 s23=5+5+1=11 s24=6+1+4=11 s25=6+2+3=11 s26=6+3+2=11 s27=6+4+1=11   p11=27n=27216=18=0.125
s1=1+5+6=12 s2=1+6+5=12 s3=2+4+6=12 s4=2+5+5=12 s5=2+6+4=12 s6=3+3+6=12 s7=3+4+5=12 s8=3+5+4=12 s9=3+6+3=12 s10=4+2+6=12 s11=4+3+5=12 s12=4+4+4=12 s13=4+5+3=12 s14=4+6+2=12 s15=5+1+6=12 s16=5+2+5=12 s17=5+3+4=12 s18=5+4+3=12 s19=5+5+2=12 s20=5+6+1=12 s21=6+1+5=12 s22=6+2+4=12 s23=6+3+3=12 s24=6+4+2=12 s25=6+5+1=12   p12=25n=25216=0.1157
p11>p12 v=11

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