SOLUTION: Two, six sided dice are rolled. Which has the highest probability? 10 ? 9 ? 7 ? 4 ? 2 ? Please help solve.

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Question 96855: Two, six sided dice are rolled. Which has the highest probability?
10 ?
9 ?
7 ?
4 ?
2 ?
Please help solve.
Found 2 solutions by edjones, Edwin McCravy:
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
If you roll 1 die the chances of any 1 number comming up is 1/6.
If you roll 2 dice 1/6*1/6=1/36 different combinations are possible.
1,1=1/36
1,2 2,1=2/36
1,3 3,1 2,2=3/36
1,4, 4,1 3,2 2,3=4/36
You can do the rest. You will find 7 is the most likely number.
Add up all the fractions after the equal signs and make sure they add up to 36/36.
Ed
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Two, six sided dice are rolled. Which has the highest probability?
10 ?
9 ?
7 ?
4 ?
2 ? 

Here are all 36 possible dice rolls:

(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)

--------------------------------------

Now I'll color code them by their sums:

(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)

The 3 red ones are the 10's, making
     P(10), the probability of rolling a 10, equal to 3/36 

The 4 blue ones are the 9's, making
     P(9), the probability of rolling a 9, equal to 4/36 

The 6 green ones are the 7's, making
     P(7), the probability of rolling a 7, equal to 6/36 

The 3 yellow ones are the 4's, making
     P(4), the probability of rolling a 4, equal to 3/36 

The pink ones is the only 2, making
     P(2), the probability of rolling a 2, equal to 1/36 

So there are more ways to roll a 7 than there are of rolling any of
the others, so it has the greatest probability, 6/36 which reduces
to 1/6.  So 7 is the correct choice.

Edwin
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