Question

When you roll two number cubes, what are the odds in simplest form against getting two numbers greater than 3?

Answer 1

`1/2 xx 1/2 =1/4`

Explanation:

On a number cube there are 6 numbers, 3 of which are greater than 3:

`1" " 2" " 3 " "color(red)(4" " 5" " 6)`

When you throw a number cube once,
Probability (number greater than 3) = `3/6 = 1/2`

The numbers on a cube cannot get "used up", so the probability of getting a number greater than 3 is `1/2` for each and every throw, irrespective of what has happened on any previous throw.

Whether you throw one cube twice or two cubes at the same time, the probability is the same:

`P(>3, >3) = P(>3) xx P(>3) =1/2 xx 1/2 =1/4`