Question

1. a standard six - sided die is rolled.

8a list all the even numbers that can be rolled, in ascending order: 2, 4, 6
8b list all the prime numbers that can be rolled, in ascending order: 2, 3, 5
8c what is the probability of rolling an even or prime number?
probability = enter your next step here

Explanation:

Step1: Identify possible outcomes

A standard six - sided die has outcomes \(1,2,3,4,5,6\). From 8a, even numbers are \(2,4,6\); from 8b, prime numbers are \(2,3,5\). The set of numbers that are even or prime is the union of these two sets. The union of \(\{2,4,6\}\) and \(\{2,3,5\}\) is \(\{2,3,4,5,6\}\). The number of elements in this set is \(n = 5\). The total number of possible outcomes when rolling a die is \(N=6\).

Step2: Calculate probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (even or prime) is \(5\) and the total number of outcomes is \(6\). So \(P = \frac{5}{6}\).

Answer:

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