Question

in an experiment, a student randomly chooses an answer to two multiple-choice questions. the first question has 3 answers to choose from, and the second question has 6 answers to choose from. how many outcomes are in the sample space? enter your numerical answer in the box.

Explanation:

Step1: Identify the counting principle

For independent events (choosing an answer for each question is independent), we use the multiplication principle. If one event has \( m \) outcomes and another independent event has \( n \) outcomes, the total number of outcomes for both events is \( m\times n \).

Step2: Apply the multiplication principle

The first question has 3 outcomes, and the second question has 6 outcomes. So the total number of outcomes in the sample space is \( 3\times6 = 18 \).

Answer:

18