Question

Two number cubes are rolled. What is the probability of rolling a number greater than 4 on
each number cube? -
P(greater than 4 on one cube)
P(greater than 4 on two cubes) = (
)
(
) =

Answer 1

If we consider each number cube on its own, we have a probability of 2/6=1/3 to get a number greater than 4: we have to roll either a 5 or a 6.

Since the two rolls are independent (i.e. the result of the first roll influences in no way the result of the second roll), if we want both rolls to return a number greater than 4, we have to multiply the probabilities:

$\dfrac{1}{3}\cdot\dfrac{1}{3}=\dfrac{1}{9}$

So, each roll has a probability of 1/3 to show a number greater than 4, which implies that the probability of getting a number greater than 4 with both rolls is 1/9.