What is the probability of getting a product of 12 from three throws of a dice?

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10 Nov 2017 Probability

What is the probability of getting a product of 12 from three throws of a dice?

OPtion

1) 12/216
2) 13/216
3) 14/216
4) 15/226
5) 16/236
6) 1/19
7) 5/72
8) 1/18
9) 16/216
10)None of these

Solution

Total Number of possible outcomes = 6C1*6C1*6C1 = 6*6*6 = 216
Positive outcomes must satisfy D1*D2*D3= 12
Below are such values of D1, D2 and D3:
1, 6, 2
1, 4, 3
1, 3, 4
1, 2, 6
2, 6, 1
2, 3, 2
2, 2, 3
2, 1, 6
3, 4, 1
3, 2, 2
3, 1, 4
4, 3, 1
4, 1, 3
6, 2, 1
6, 1, 2

Count of positive outcome = 15
Probability = Positive outcome/Total Possible Outcomes = 15/216 = 5/72
Option 7)

Correct Option: 7 Best Solution (2)

Dr.Dipin Singh   7 years AGO

Total possible combinations = 6x6x6=216
Favourable combinations are ... 1,2,6 ( 6 combinations), 1,3,4 ( 6 combinations) and 2,2,3 ( 3 Combinations).. total 15 combinations.
Probability of getting product of 12 with 3 dice = 15/216= 5/72

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Varun   7 years AGO

Possible dice combinations are :
1 2 6 × 6
1 3 4 × 6
2 2 3 × 3
Total 15
Possible dice combination = 6×6×6 =216
So, probability = 15/216
Divide and multiply by 3.
Probability = 5/72

Like? Yes (7) | No (6)