Question

a die is rolled. find the probability of the given event. write your answers as whole numbers or simplified fractions. a. the number showing is a 6 ( p(6)=) b. the number showing is an even number ( p(\text { even })=) c. the number showing is greater than 2 ( p(\text { greater than } 2)= )

Explanation:

Step1: Determine total number of outcomes

A die has 6 faces. So, total number of outcomes \( n(S)=6 \).

Step2: Calculate \( P(6) \)

There is only 1 face with 6. So, number of favorable outcomes \( n(6) = 1 \).
Using the probability formula \( P(A)=\frac{n(A)}{n(S)} \), we get \( P(6)=\frac{1}{6} \).

Step3: Calculate \( P(\text{even}) \)

Even numbers on a die are 2, 4, 6. So, number of favorable outcomes \( n(\text{even})=3 \).
Using the probability formula \( P(A)=\frac{n(A)}{n(S)} \), we get \( P(\text{even})=\frac{3}{6}=\frac{1}{2} \).

Step4: Calculate \( P(\text{greater than }2) \)

Numbers greater than 2 on a die are 3, 4, 5, 6. So, number of favorable outcomes \( n(\text{greater than }2)=4 \).
Using the probability formula \( P(A)=\frac{n(A)}{n(S)} \), we get \( P(\text{greater than }2)=\frac{4}{6}=\frac{2}{3} \).

Answer:

A. \( \frac{1}{6} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)