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

consider the roll of a six - sided die. choose all that are correct.\na probability of an even number is $\frac{1}{2}$\nb probability of a 1 or 5 is $\frac{1}{3}$\nc probability of a number less than 3 is $\frac{1}{2}$\nd probability of a 2 or an odd number is $\frac{2}{3}$
Answer
Explanation:
Step1: Calculate total outcomes
A six - sided die has 6 possible outcomes: 1, 2, 3, 4, 5, 6.
Step2: Analyze option A
Even numbers on a six - sided die are 2, 4, 6. So number of favorable outcomes = 3. Probability = $\frac{3}{6}=\frac{1}{2}$.
Step3: Analyze option B
Numbers 1 or 5 are 2 favorable outcomes. Probability = $\frac{2}{6}=\frac{1}{3}$.
Step4: Analyze option C
Numbers less than 3 are 1, 2. So number of favorable outcomes = 2. Probability = $\frac{2}{6}=\frac{1}{3}\neq\frac{1}{2}$.
Step5: Analyze option D
Odd numbers are 1, 3, 5 and we add 2. So number of favorable outcomes = 4. Probability = $\frac{4}{6}=\frac{2}{3}$.
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 $\frac{2}{3}$