Simple probability question

[299678]

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Q. two normal dice are rolled. What is the probability of getting a sum less than 10?

probability more than 10 = 1/6
1-(1/6) = 5/6

Anybody can explain me logically why (2,3) (3,2) counted twice
but (6.6) only counted once?

 

[Streetwolf]

Q. two normal dice are rolled. What is the probability of getting a sum less than 10?

probability more than 10 = 1/6
1-(1/6) = 5/6

Anybody can explain me logically why (2,3) (3,2) counted twice
but (6.6) only counted once?

Roll two dice and try to get (6,6) in two different ways.

 

[DATlongshui]

I don't understand your question, can you make it more clear as to the question?
The way I solved this question is:
Probability of getting sum less than 10= 1-probability of getting sum more or equal to 10
Three situations to get sum >=10:
dice 1=4 , dice2=6 (P=1/6X1/6)
dice 1=5, dice2=5 or 6 (P=1/6X2/6)
dice 1=6, dice2=4, 5, or 6 (P=1/6X3/6)
since it is two normal(identical) dices, order/arrangement will not be considered, only combination considered (i.e. no need to double the above probability)
Taken together, P(sum of getting >=10)=1/6(1/6+2/6+3/6)=1/6
so P(sum of getting less than 10)=1-1/6=5/6

 

[RUpremed]

here is a way to look at it...

suppose you roll the die, and one of the die always reads 1..


1+1=2
1+2=3 TOTAL # possibilities: 6
1+3=4
1+4=5
1+5=6
1+6=7

do the same with 2,3,4,5, 6 (don't count doubles because you're considering the sum of the die)

2+2=4
2+3=5
2+4=6 TOTAL # possibilities: 5
2+5=7
2+6=8

you'll notice a pattern as it goes along so eventually you'll have 6+5+4+3+2+1=21 (this is the total number of combinations you can get)

then count the sums that are less than 10: 17...17/21=81%

 

[RUpremed]

idk if my approach is correct though...but it is close to 5/6=83%?

 

[Streetwolf]

idk if my approach is correct though...but it is close to 5/6=83%?

No it's wrong. You have to consider doubles because of the OP's original question.

You have two dice:

A and B

1 and 1
1 and 2
2 and 1
1 and 3
3 and 1
1 and 4
4 and 1
1 and 5
5 and 1
1 and 6
6 and 1
2 and 2
2 and 3
3 and 2
2 and 4
4 and 2
2 and 5
5 and 2
2 and 6
6 and 2
3 and 3
3 and 4
4 and 3
3 and 5
5 and 3
3 and 6
6 and 3
4 and 4
4 and 5
5 and 4
4 and 6
6 and 4
5 and 5
5 and 6
6 and 5
6 and 6

So you see that there IS a difference between (5,6) and (6,5) because it matters which die rolls which number.

Of all those possibilities it just so happens that the first 30 in a row are the ones that are under a sum of 10. And that would be 5/6 of the numbers.