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# In throwing 3 dice. What is the probability of getting a sum of 13?

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In throwing 3 dice. What is the probability of getting a sum of 13?

Guest Nov 21, 2014

#2
+92674
+10

I believe the probability of 13 is:

6 6 1   3 ways to do this

6 5 2   6 ways to do this

6 4 3   6 ways to do this

5 5 3   3 ways to do this

5 4 4   3 ways to do this   =

21 total ways to roll a 13

So....the probability is

21 / 216  = 0.0972222222222222  = about 10%

CPhill  Nov 21, 2014
#1
+94105
+10

1+12       1+6+6                             1 way

2+11        2+5+6    2=6+5               2 ways

3+10        10=6+4 or 4+6, or 5+5       3 ways

4+9          9=6+3, 3+6, 5+4, 4+5         4 ways

5+8          8=6+2, 2+6, 5+3, 3+5, 4+4   5 ways

6+7        7=6+1, 1+6, 5+2, 2+5, 4+3, 3+4  6 ways

6+5+4+3+2+1=21

Total combinations  $${{\mathtt{6}}}^{{\mathtt{3}}} = {\mathtt{216}}$$

P(sum of 13) = $${\frac{{\mathtt{21}}}{{\mathtt{216}}}} = {\frac{{\mathtt{7}}}{{\mathtt{72}}}} = {\mathtt{0.097\: \!222\: \!222\: \!222\: \!222\: \!2}}$$

Melody  Nov 21, 2014
#2
+92674
+10

I believe the probability of 13 is:

6 6 1   3 ways to do this

6 5 2   6 ways to do this

6 4 3   6 ways to do this

5 5 3   3 ways to do this

5 4 4   3 ways to do this   =

21 total ways to roll a 13

So....the probability is

21 / 216  = 0.0972222222222222  = about 10%

CPhill  Nov 21, 2014
#3
+94105
+5

Yes your way is neat too Chris :)

Melody  Nov 21, 2014
#4
+92674
+5

Thanks......hey .....we actually agree on 2 probabilty problems......what's the probability ???

CPhill  Nov 21, 2014
#5
+94105
0

Not real high.  We must be sick.  This is a real anomoly.  LOL

Melody  Nov 21, 2014
#6
+92674
0

Yep......out of our minds !!!! LOL!!!

CPhill  Nov 21, 2014
#7
+7188
0

Woah....wait....what???

happy7  Nov 21, 2014
#8
+92674
0

It's an old joke between us, happy7......Melody and I are known to give some very "creative" answers to probability questions........some of them even turn out to be correct.....!!!!

CPhill  Nov 21, 2014