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

Explanation:

Step1: Identify sample space

A standard six - sided die has outcomes \(S=\{1,2,3,4,5,6\}\), so \(n(S) = 6\).

Step2: Find set of even or prime numbers

From 6a, even numbers \(E=\{2,4,6\}\). From 6b, prime numbers \(P = \{2,3,5\}\).
Using the formula for the union of two sets \(E\cup P=\{2,3,4,5,6\}\) (we take each unique element from \(E\) and \(P\)).
The number of elements in \(E\cup P\), \(n(E\cup P)=5\).

Step3: Calculate probability

The formula for probability \(P(A)=\frac{n(A)}{n(S)}\), where \(A = E\cup P\).
So \(P(E\cup P)=\frac{5}{6}\).

Answer:

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