Question

a fair dice with pips representing the numbers 1, 2, and 6 is rolled.
a. what is the probability of rolling an even number? express the probability as a fraction, decimal, and percent.
b. what is the probability of rolling a factor of six? express the probability as a fraction, decimal, and percent.
c. is it more likely that someone will roll an even number or a factor of six? explain.

Explanation:

Step1: Identify total outcomes

A fair - dice has 6 possible outcomes when rolled.

Step2: Find even - numbered outcomes for part a

The even numbers on a dice are 2, 4, 6. But since our dice has numbers 1, 2, 6 only, the even - numbered outcomes are 2 and 6. So there are 2 even - numbered outcomes.
The probability $P(\text{even})$ as a fraction is $\frac{2}{6}=\frac{1}{3}$. As a decimal, $\frac{1}{3}\approx0.333$. As a percent, $0.333\times100 = 33.3\%$.

Step3: Find factors of six for part b

The factors of 6 are 1, 2, 3, 6. For our dice with numbers 1, 2, 6, there are 3 factors of 6.
The probability $P(\text{factor of 6})$ as a fraction is $\frac{3}{6}=\frac{1}{2}$. As a decimal, $\frac{1}{2}=0.5$. As a percent, $0.5\times100 = 50\%$.

Step4: Compare probabilities for part c

We have $P(\text{even})=\frac{1}{3}\approx0.333$ and $P(\text{factor of 6})=\frac{1}{2}=0.5$. Since $0.5>0.333$, it is more likely to roll a factor of 6.

Answer:

a. $\frac{1}{3}$, $0.333$, $33.3\%$
b. $\frac{1}{2}$, $0.5$, $50\%$
c. It is more likely to roll a factor of 6 because the probability of rolling a factor of 6 ($0.5$) is greater than the probability of rolling an even number ($0.333$).