What is the probability of getting a sum 13 from three throws of a dice?

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03 Mar 2017 Probability

What is the probability of getting a sum 13 from three throws of a dice?

OPtion

1) 11/108
2) 7/72
3) 1/9
4) 25/216
5) 13/108
6) 6/54
7) 7/54
8) 29/216
9) 5/54
10)31/216

Solution

Total Number of possible outcomes = 6C1*6C1*6C1 = 6*6*6 = 216
Positive outcomes must satisfy D1+D2+D3= 13
(1,6,6) (2,6,5) (2,5,6) (3,6,4) (3,5,5) (3,4,6) (4,6,3) (4,5,4) (4,4,5) (4,3,6) (5,6,2) (5,5,3) (5,4,4) (5,3,5) (5,2,6) (6,5,2) (6,4,3) (6,3,4) (6,2,5) (6,1,6) and (6,6,1)
Count of positive outcome = 21
Probability = Positive outcome/Total Possible Outcomes = 21/216 = 7/72
Option 2)

Correct Option: 2 Best Solution (8)

sudhir saurav   7 years AGO

just count the number of ways to get 13.
we just need to count possibilities for two dice because the 3rd dice value is fixed. for two dice, the sum can be anywhere from 7 to 12 and that would be 6+5+4+3+2+1=21
so probability is 21/216=7/72

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G.S.Kantharao   7 years AGO

No of out comes =6*6*6 = 216
Required out comes =(1,6,6),(2,,5,6),(2,6,5),(3,4,6),(3,5,5),(3,6,4),(4,3,6),(4,4,5),(4,5,,4),(4,6,3),(5,2,6),(5,3,5),(5,4,4),(5,5,3),(5,6,2),(6,1,6),(6,2,5),(6,3,4),(6,4,3),(6,5,2),(6,6,1)
Total required out comes = 21
Probability = 21/216 = 7/72
So the right answer is 7/72 which stands with option 2.

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Devendra Marghade   7 years AGO

Total outcomes=6x6x6= 216
Favorable outcomes=(1,6,6)(2,5,6)(2,6,5)(3,4,6)(3,5,5)(3,6,4)(4,3,6)(4,4,5)(4,5,4)(4,6,3)(5,2,6)(5,3,5)(5,4,4)(5,5,3)(5,6,2)(6,1,6)(6,2,5)(6,3,4)(6,4,3)(6,5,2)(6,6,1)=Total 21
So probability=21/216= 7/72
Option 2)

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Gaurav kumar   7 years AGO

{1,6,6}=3!/1!
{2,5,6}=3!/1!
{3,4,6},{3,5,5}=3!/2!
{4,4,5}=3!/1!
sum=21
3 dice is =216
21/216=7/72

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palak Jain   7 years AGO

sum must be 13 on the throw of three dices
cases:
(1,6,6)=arrangement=3 (1,6,6) (6,1,6) (6,6,1)
(2,5,6)=arrangement = 3!=6
(3,4,6)=arrangement=3!=6
(4,4,5)=arrangement=3
(5,5,3)=arrangement=3
total =21/6*6*6=21/216=7/72

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himabindu   7 years AGO

the total no.of outcomes is 6*6*6=216
the no.of ways to get a 13 is 21
probability= 21/216 = 7/72
(1,6,6)= 3!/2!=3
(2,5,6)= 3!=6
(3,4,6) = 3!=6
(3,5,5)= 3!/2!=3
(4,4,5)= 3!/2!=3

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Harsh Poddar   7 years AGO

Total possible outcome= 6×6×6=216
Sum =13
(1,6,6)-3 ways
(2,5,6)-6 ways
(3,5,5)-3 ways
(3,4,6)-6 ways
(4,4,5)-3 ways
Total ways=21
Probability =21/216=7/72
Option 2

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kunal gupta   7 years AGO

total favorable outcomes=21
probability=21/216=7/72

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