Question

1. a standard six - sided die is rolled.

6a list all the even numbers that can be rolled, in ascending order: 2, 4, 6
6b list all the prime numbers that can be rolled, in ascending order: 2, 3, 5
6c what is the probability of rolling an even or prime number?
probability = enter your next step here

Explanation:

Step1: Identify sample space and events

Sample space \( S = \{1,2,3,4,5,6\} \), so \( n(S)=6 \).
Let \( A \) be event of rolling even: \( A = \{2,4,6\} \), \( n(A)=3 \).
Let \( B \) be event of rolling prime: \( B = \{2,3,5\} \), \( n(B)=3 \).
Intersection \( A \cap B = \{2\} \), \( n(A \cap B)=1 \).

Step2: Apply inclusion - exclusion principle

For \( P(A \cup B) \), formula is \( P(A \cup B)=\frac{n(A)+n(B)-n(A \cap B)}{n(S)} \).
Substitute values: \( \frac{3 + 3-1}{6}=\frac{5}{6} \).

Answer:

\(\frac{5}{6}\)