Question

1. explain how you could predict the number of times you will roll a multiple of 3 on a number cube in 30 rolls.

Explanation:

Step1: Determine probability of rolling a multiple of 3

A number cube has 6 faces numbered 1 - 6. Multiples of 3 are 3 and 6. So the probability $P$ of rolling a multiple of 3 in one roll is $\frac{2}{6}=\frac{1}{3}$.

Step2: Use probability to predict number of times in 30 rolls

We use the formula $n = P\times N$, where $n$ is the number of times we expect the event to occur, $P$ is the probability of the event, and $N$ is the total number of trials. Here, $P=\frac{1}{3}$ and $N = 30$. So $n=\frac{1}{3}\times30 = 10$.

Answer:

We first find the probability of rolling a multiple of 3 on a single roll of a number - cube, which is $\frac{1}{3}$. Then we multiply this probability by the total number of rolls (30). We would predict to roll a multiple of 3 about 10 times in 30 rolls.