Three dice are tossed. What is the probability that the sum is less than 5?

Answer 1

1/54 (for 6-sided dice of course)
There are 6*6*6 = 216 possible outcomes, and
1,1,1
1,1,2
1,2,1
2,1,1
are the only outcomes with sum<5, so 4/216 = 1/54

Answer 2

If three dice are tossed, there are 6 possibilities for the first die, 6 for the second, and 6 for the 3rd, for a total of 216 (6x6x6) possible outcomes.

Of those outcomes, to have the sum less than 5, it would have to be either a 4 or a 3 (because 1+1+1 is the least you can get).

This can only happen 4 ways: (1,1,1) (1,1,2) (1,2,1) (2,1,1).

So the probability that the sum is less than 5 is 4/216 = 1/54.

Answer 3

Combinations for throwing three dice:
1+1+1=3
1+1+2=4
1+1+3=5
1+1+4=6
1+1+5=7
1+1+6=8
1+2+2=5
1+2+3=6
1+2+4=7
1+2+5=8
1+2+6=9
1+3+3=7
1+3+4=8
1+3+5=9
1+3+6=10
1+4+4=9
1+4+5=10
1+4+6=11
1+5+5=11
1+5+6=12
1+6+6=13
2+2+2=6
2+2+3=7
2+2+4=8
2+2+5=9
2+2+6=10
2+3+3=8
2+3+4=9
2+3+5=10
2+3+6=11
2+4+4=10
2+4+5=11
2+4+6=12
2+5+5=12
2+5+6=13
2+6+6=14
3+3+3=9
3+3+4=10
3+3+5=11
3+3+6=12
3+4+4=11
3+4+5=12
3+4+6=13
3+5+5=13
3+5+6=14
3+6+6=15
4+4+4=12
4+4+5=13
4+4+6=14
4+5+5=14
4+5+6=15
4+6+6=16
5+5+5=15
5+5+6=16
5+6+6=17
6+6+6=18

This means that there are 56 total combinations possible. Now we can count how many are less than 5 (this doesn't include 5's). I counted 2 of them to be less than 5. That makes our chances 2 in 56. This reduces to a 1 in 28 chance (approximately 3.57%). Please note that I didn't use the probibility of each die, because that's not what the question said. It was concerned with "three dice". It doesn't matter which die is a 1, or anything of that sort, just the sum of the dice. I hope that made sense.

Answer: The probibility that the sum will be less than five is 1 in 28 (1 / 28) or approximately 3.57%.

Answer 4

There are 6x6x6=216 possible combinations.

The only combinations that sum to less than 5 are:

111, 112, 121 and 211, or 4/216=1/54.

Answer 5

the answer is 2

Answer 6

I suck at probability, but I think this is how you do it:
The first die has a probability of 1/6 that it will be a 1.
The second has the same.
The third can be a one or a two so that it adds up to four so it has a probability of 2/6 or 1/3.
You multiply them all together 1/6 *1/6 * 1/3 = 1/108.

Answer 7

1 x 1 x 2: 6 x 6 x 6
2: 216
1:108

Answer 8

I'll let the math gurus here beat me up, but here is my thinking...I'm just a paramedic... only one side per six sided die can show... so its 3 per 18 no matter what combination... 1/6th or about a 17% chance.