The chance of having at least one 6 when you throw with six dices

How big is the chance that, when you roll six dices, you will have AT LEAST one six ?

And how do you calculate this ?

### 1 Answer | Add Yours

Consider a 3 dice example. If you understand this example, then you can increase the number of dice.

Roll the dice and compute the chances of a six not appearing on the first die: 5/6

Multiply this fraction by the chances of a six not appearing on the second die:

5/6*5/6 = 25/36

Multiply this fraction by the chances of a six not appearing on the third die:

25/36*5/6 = 125/216

To find out the chances of a six to appear on the three dice, subtract 125 from 216.

216-125=91

91 chances out of 216 for a six to appear on the three dice.

To find out the chances of a six to appear on the six dice, subtract 125 from 216.

125/216*125/216 = 15625/46656

46656-15625=31031

**ANSWER: 31031 chances out of 46656 for a six to appear on the six dice.**

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