probability to get a pair (dices)

**Anna55** · April 30th 2011, 10:58 AM

You have five dices. What is the probability that you will get a pair on one roll?

**pickslides** · April 30th 2011, 02:01 PM

Originally Posted by Anna55

You have five dices. What is the probability that you will get a pair on one roll?

Let me get this straight, you have 5 die. If you roll them all at once, what is the probability you will get exactly one pair from the 5? Or if 3, 4, or 5 of the same number is rolled then this is also considered a pair?

**Plato** · April 30th 2011, 02:04 PM

Originally Posted by Anna55

You have five dices. What is the probability that you will get a pair on one roll?

Lets find the probability of no pairs.
All five dice are different.
There are six ways out of six for the first die to be different.
There are five ways out of six for the second die to be different.
There are four ways out of six for the third die to be different.
etc.

That would be $\frac{6}{6}\cdot\frac{5}{6}\cdot\frac{4}{6}\cdot \frac{3}{6}\cdot\frac{2}{6}=\frac{120}{6^4}$

The opposite of none is at least one.

**Soroban** · April 30th 2011, 04:04 PM

Hello, Anna55!

One cube is called a die.
The plural is dice.

You have five dice. What is the probability that you will get a pair on one roll?

If you mean exactly One Pair, the solution is more elaborate.

$\text{There are: }\,6^5\,=\,7776\text{ possible outcomes.}$

We have 6 choices for the value of the Pair.

$\text{There are: }{5\choose2} = 10\text{ choices for the two dice to have the Pair.}$

The other three dice must have values which are
. . different from the Pair and from each other.

. . $\text{There are: }\:5\cdot4\cdot3 \,=\,60\text{ ways.}$

$\text{Hence, there are: }\:6\cdot10\cdot60 \:=\:3600\text{ ways to have exactly One Pair.}$

$\text{Therefore: }\:P(\text{exactly One Pair}) \;=\;\frac{3600}{7776} \;=\;\frac{25}{54}$

**Plato** · April 30th 2011, 05:34 PM

Originally Posted by Soroban

[size=3][size=3]
If you mean exactly One Pair, the solution is more elaborate.

How can "You have five dices. What is the probability that you will get a pair on one roll?" mean exactly one pair?

**mr fantastic** · April 30th 2011, 11:06 PM

Originally Posted by Soroban

Hello, Anna55!

One cube is called a die.
The plural is dice.

[snip]

Unless you're name is Jinks, in which case you would hate those miserable dices (or should I say "hate those miserable deeces to pieces" ....)

**Anna55** · May 1st 2011, 12:29 AM

Originally Posted by pickslides

Let me get this straight, you have 5 die. If you roll them all at once, what is the probability you will get exactly one pair from the 5? Or if 3, 4, or 5 of the same number is rolled then this is also considered a pair?

If you have 2, 4, or 5 of the same number, that is also considered to be a pair.

**Anna55** · May 1st 2011, 04:09 AM

Thank you everybody for your help and time! I understand it now.
1-(120/6^4)=49/54

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