Is it rare to get a 4 when rolling a pair of die?

Question

This is for a astatistics class

Forgive me for saying. Just getting one 4 by rolling a pair of die, not a sum of 4. Thanks!

Forgive me for saying. Just getting one 4 by rolling a pair of die, not a sum of 4. Thanks!

Rare defined as .05 probability or less

Answer 1

According to your additional comments, you are *not* asking about the sum being 4, you are asking about exactly one 4 appearing on either die. This is a different answer than what most people are answering. The correct answer is given below:

There are 36 ways to roll the dice:

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

You can easily see there are 10 combinations out of 36 that result in one 4. So the probability is 10/36 or 5/18.

Mathematically it would be (1/6)(5/6)(2!): Chance of a four (1/6), times the chance of a non-four (5/6), times the ways to arrange these two combinations (2!). This is 10/36 or 5/18, just the same answer as if you counted.

This comes out to about 27.778% of the time, which is larger than your 5% threshold for "rare". So the answer is "no" this is not a rare event.

Answer 2

Mathematically yes, but not as rare as other combinations.

Heres your combinations:

1+1 2+1 3+1 4+1 5+1 6+1
1+2 2+2 3+2 4+2 5+2 6+2
1+3 2+3 3+3 4+3 5+3 6+3
1+4 2+4 3+4 4+4 5+4 6+4
1+5 2+5 3+5 4+5 5+5 6+5
1+6 2+6 3+6 4+6 5+6 6+6



X=a+b

x=total
a=dice a
b=dice b

a={1,2,3,4,5,6}
b={1,2,3,4,5,6}

Therefore:
there are 36 combinations, but only 3 total 4

3\36 or 1\12 is the probability

Answer 3

You have two dice. Each side has a 1 in 6 chance of showing up. You can get a 4 by rolling: 1 & 3, or 2 & 2.

Rolling a 1 and a 3 is a 1/36 chance. (1/6 * 1/6)

Rolling a 2 and a 2 is a 1/36 chance. (1/6 * 1/6)
Rolling a 3 and a 1 is a 1/36 chance.

So rolling a 4 (by rolling a 1&3 OR 2&2 OR 3&1) is a 3/36 or 1/12 chance.
(1/36 + 1/36 +1/36)

This is a 8.3% chance, or about 8 times out of 100 rolls will be a total of 4.

Answer 4

I wouldn't say rare, but the odds are 1/12. There are three different ways to get a 4 (1-3, 2-2, 3-1). There are 36 total combinations of the dice. That gives you a 3/36 shot, or 1/12.

Answer 5

since each dice is independant of the other, lets think of it as the same expirement repeated twice...

the chance of getting any particular face (in this case a 4) on a die is 1/6 (because we're intrested in 1 face, and there are a total of 6 faces).

so if we were to roll 1 die, we would have a 1/6 chance of getting a four. but we're rolling 2 dice, so we're going to multiply this by 2.

1/6 * 2 = 2/6

2/6 is greater than 0.05, so it is not statistically rare that this would happen.

Answer 6

The probability of exactly one 4 is 2(1/6)(5/6) = 10/36 = 5/18 = .27777 (the 7 is repeating), so it is not rare.
The probability of at least one 4 is
(1/6)(1/6) + (2)(1/6)(5/6) = 1/36 + 10/36 = 11/36

Answer 7

hey
u got a total of 36 combinations
out of these...u can get a 4 in 11 cases :
1-4
2-4
3-4
4-4
5-4
6-4
4-1
4-2
4-3
4-5
4-6
which means that the probability is: 11/36=0.305 ..which is about 1 in 3 as another user earlier said

Answer 8

odds probability of numbers of a pair of six sided dies are as follows:

2 = 1 in 36
3 = 1 in 18
4 = 1 in 12
5 = 1 in 9
6 = 1 in 7.2
7 = 1 in 6
8 = 1 in 7.2
9 = 1 in 9
10 = 1 in 12
11 = 1 in 18
12 = 1 in 36

the answer for your revised question would be 1 in 3.6 or 27.7%chance of just rolling one 4

Answer 9

The chance to get one 4 with two dice is 1/6+1/6-1/36 = ~0.30555555
The chance to get two 4s is of-course 1/36 = ~0.02777777
The chance to get at-least one 4 is those two combined, which is 1/3 = ~0.333333

Not different from the chance to get any other number...

Answer 10

yes but it is possible for u to roll a 4 with 2 dice