Aptitude - Probability - Discussion

As we know one dice has 6 sides(4 edges + 1frontside + 1backside = 6)
Possibilities of getting sum 9 are (6,3)(5,4)(4,5)(3,6) i.e 4 possibilities.
Because;
6+3 = 9
5+4 = 9
4+5 = 9
3+6 = 9.

Remember! The numbers you add should not exceed the 6 digit.

Solution for your question is @Dhaval.
4/6 * 6 * 6 = 4/216 or 1/54.
Hope,This Helps!

One dice means 6 faces.
Two dice means 6 * 6 = 36 faces.
Either,
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
Total = 36 outcomes.
So question ask that,
Sum =9.
So,
3 + 6 = 9 (3,6)
6 + 3 = 9 (6,3)
4 + 5 = 9 (4,5)
5 + 4 = 9 (5,4)
4 out comes.
p = num of outcomes/total outcomes.
p = 4/36 = 1/9.

Hope you understand this.

Here how could you consider (5, 4) and (4, 5) two different events? Please explain.

(1/8) is also possible for the answer. Right?

Why not taking the case {3,3}? Please explain me.

@Pooja Gm.

Dice does not have 8 surfaces it has only 6.

At first you draw sample space then you find pair which sum is 9, (1,1), (1,2),....... (5,4), (6,3),(3,6), (4,5).

Total pair 36 and sum of 9 pair is 4 them p(sum 9)= 4 ÷ 36 = 1/9.

Why we should not use the permutations here?like sum 9 can appear in either (6, 3) or (3, 6) , (5, 4) or (4, 5). Why we only choose the one possibility?

Look in a dice there are number 1, 2, 3, 4, 5, 6.

To form as a 9 we need 6 + 5 + 4 + 3 number. Such as 5 + 4 = 9, 6 + 3 = 9 but 1 + 8 or 2 + 7 is not possible because dice do not contain the number 7, 8.

So sum up the number 6 +5 + 4 + 3 = 18 (one dice). 18 * 2 = 36 (two dice).

Sum 9 means (1,8)(2,7)(3,6)(4,5)(5,4)(6 3)(7,2).

Means 8/36 = 2/9.