a die is rolled once. find the probabilities of the given events. leave your answer as a reduced…

Explanation:

Step1: Determine total outcomes

A standard die has 6 faces, so total number of outcomes $n(S)=6$.

Step2: Calculate probability for part a

The event of rolling a 4 has 1 favorable outcome $n(A) = 1$. Probability $P(A)=\frac{n(A)}{n(S)}=\frac{1}{6}$.

Step3: Calculate probability for part b

Even - numbered faces on a die are 2, 4, 6. So $n(B)=3$. Probability $P(B)=\frac{n(B)}{n(S)}=\frac{3}{6}=\frac{1}{2}$.

Step4: Calculate probability for part c

Numbers greater than 1 on a die are 2, 3, 4, 5, 6. So $n(C)=5$. Probability $P(C)=\frac{n(C)}{n(S)}=\frac{5}{6}$.

Answer:

a. $\frac{1}{6}$ b. $\frac{1}{2}$ c. $\frac{5}{6}$