On a roll of dice, what is the probability of rolling either a multiple of 4 or a multiple of 6?

1 Answer

#7/18#

Explanation:

Here is a table of what can be rolled:

#((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(1|,2,3,4,5,6,7),(2|,3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,12))#

Let's take all the multiples of 6, add it to the multiples of 4, subtract out the duplicates, and that will give us the number of ways we can satisfy the condition of the question.

For 6s - we can have 6 and 12. There are 5 ways to get a 6 and 1 way to get a 12 - this gives 6 multiples.

For 4s - we can have 4, 8, and 12. There are 3 ways to get 4, 5 ways to get 8, and one way to have 12 - this gives 9 multiples.

There is one duplicate: 12, and so we need to subtract 1.

We then get: #6+9-1=14#

There are 36 rolls in total possible, so the resulting probability is:

#14/36=7/18#