consider the roll of a six - sided die. choose all that are correct. a probability of an even number is 1/2…

Answer:

A. probability of an even number is $\frac{1}{2}$ B. probability of a 1 or 5 is $\frac{1}{3}$ D. probability of a 2 or an odd number is $\frac{2}{3}$

Explanation:

Step1: Define sample - space

The sample - space when rolling a six - sided die is $S={1,2,3,4,5,6}$, and $n(S) = 6$.

Step2: Analyze option A

Even numbers are ${2,4,6}$, $n(\text{even})=3$. Probability $P(\text{even})=\frac{n(\text{even})}{n(S)}=\frac{3}{6}=\frac{1}{2}$.

Step3: Analyze option B

Numbers 1 or 5: ${1,5}$, $n({1,5}) = 2$. Probability $P(1\text{ or }5)=\frac{n({1,5})}{n(S)}=\frac{2}{6}=\frac{1}{3}$.

Step4: Analyze option C

Numbers less than 3 are ${1,2}$, $n(\text{less than }3)=2$. Probability $P(\text{less than }3)=\frac{n(\text{less than }3)}{n(S)}=\frac{2}{6}=\frac{1}{3}\neq\frac{1}{2}$.

Step5: Analyze option D

2 or odd numbers: ${1,2,3,5}$, $n({1,2,3,5}) = 4$. Probability $P(2\text{ or odd})=\frac{n({1,2,3,5})}{n(S)}=\frac{4}{6}=\frac{2}{3}$.