Question

Use the Counting Principle to find the probability of rolling a 4 on each of 3 number cubes

Answer 1

Answer:

$\frac{1}{216}$

Step-by-step explanation:

We have been given that three cubes are being rolled and we are required to find the probability of getting 4 on each of the three cubes.

We know the probability of rolling a 4 on one cube will be $\frac{1}{6}$. Since there are 3 cubes, the probability of rolling 4 in each of the individual cubes will be $\frac{1}{6}$.

But we want 4 to be rolled on all three cubes at once, in order for that to happen, we need to get a four on first cube AND second cube AND third cube. Since there is AND between the events, we will multiplied their probabilities as per counting principle. Thus, the required probability of rolling 4 on each of the three cubes is $\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{6}$ which simplifies to $\frac{1}{216}$.